Calculus Examples

$\int_{0}^{10} x^{2} {(\sqrt{x} + 7)}^{2} d x$

Step 1

Simplify.

Tap for more steps...

Step 1.1

Rewrite ${(\sqrt{x} + 7)}^{2}$ as $(\sqrt{x} + 7) (\sqrt{x} + 7)$ .

$\int_{0}^{10} x^{2} ((\sqrt{x} + 7) (\sqrt{x} + 7)) d x$

Step 1.2

Expand $(\sqrt{x} + 7) (\sqrt{x} + 7)$ using the FOIL Method.

Tap for more steps...

Step 1.2.1

Apply the distributive property.

$\int_{0}^{10} x^{2} (\sqrt{x} (\sqrt{x} + 7) + 7 (\sqrt{x} + 7)) d x$

Step 1.2.2

Apply the distributive property.

$\int_{0}^{10} x^{2} (\sqrt{x} \sqrt{x} + \sqrt{x} \cdot 7 + 7 (\sqrt{x} + 7)) d x$

Step 1.2.3

Apply the distributive property.

$\int_{0}^{10} x^{2} (\sqrt{x} \sqrt{x} + \sqrt{x} \cdot 7 + 7 \sqrt{x} + 7 \cdot 7) d x$

Step 1.3

Simplify and combine like terms.

Tap for more steps...

Step 1.3.1

Simplify each term.

Tap for more steps...

Step 1.3.1.1

Multiply $\sqrt{x} \sqrt{x}$ .

Tap for more steps...

Step 1.3.1.1.1

Raise $\sqrt{x}$ to the power of $1$ .

$\int_{0}^{10} x^{2} ({\sqrt{x}}^{1} \sqrt{x} + \sqrt{x} \cdot 7 + 7 \sqrt{x} + 7 \cdot 7) d x$

Step 1.3.1.1.2

Raise $\sqrt{x}$ to the power of $1$ .

$\int_{0}^{10} x^{2} ({\sqrt{x}}^{1} {\sqrt{x}}^{1} + \sqrt{x} \cdot 7 + 7 \sqrt{x} + 7 \cdot 7) d x$

Step 1.3.1.1.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\int_{0}^{10} x^{2} ({\sqrt{x}}^{1 + 1} + \sqrt{x} \cdot 7 + 7 \sqrt{x} + 7 \cdot 7) d x$

Step 1.3.1.1.4

Add $1$ and $1$ .

$\int_{0}^{10} x^{2} ({\sqrt{x}}^{2} + \sqrt{x} \cdot 7 + 7 \sqrt{x} + 7 \cdot 7) d x$

Step 1.3.1.2

Rewrite ${\sqrt{x}}^{2}$ as $x$ .

Tap for more steps...

Step 1.3.1.2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

$\int_{0}^{10} x^{2} ({(x^{\frac{1}{2}})}^{2} + \sqrt{x} \cdot 7 + 7 \sqrt{x} + 7 \cdot 7) d x$

Step 1.3.1.2.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\int_{0}^{10} x^{2} (x^{\frac{1}{2} \cdot 2} + \sqrt{x} \cdot 7 + 7 \sqrt{x} + 7 \cdot 7) d x$

Step 1.3.1.2.3

Combine $\frac{1}{2}$ and $2$ .

$\int_{0}^{10} x^{2} (x^{\frac{2}{2}} + \sqrt{x} \cdot 7 + 7 \sqrt{x} + 7 \cdot 7) d x$

Step 1.3.1.2.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.3.1.2.4.1

Cancel the common factor.

$\int_{0}^{10} x^{2} (x^{\frac{2}{2}} + \sqrt{x} \cdot 7 + 7 \sqrt{x} + 7 \cdot 7) d x$

Step 1.3.1.2.4.2

Rewrite the expression.

$\int_{0}^{10} x^{2} (x^{1} + \sqrt{x} \cdot 7 + 7 \sqrt{x} + 7 \cdot 7) d x$

Step 1.3.1.2.5

Simplify.

$\int_{0}^{10} x^{2} (x + \sqrt{x} \cdot 7 + 7 \sqrt{x} + 7 \cdot 7) d x$

Step 1.3.1.3

Move $7$ to the left of $\sqrt{x}$ .

$\int_{0}^{10} x^{2} (x + 7 \cdot \sqrt{x} + 7 \sqrt{x} + 7 \cdot 7) d x$

Step 1.3.1.4

Multiply $7$ by $7$ .

$\int_{0}^{10} x^{2} (x + 7 \sqrt{x} + 7 \sqrt{x} + 49) d x$

Step 1.3.2

Add $7 \sqrt{x}$ and $7 \sqrt{x}$ .

$\int_{0}^{10} x^{2} (x + 14 \sqrt{x} + 49) d x$

Step 1.4

Apply the distributive property.

$\int_{0}^{10} x^{2} x + x^{2} (14 \sqrt{x}) + x^{2} \cdot 49 d x$

Step 1.5

Simplify.

Tap for more steps...

Step 1.5.1

Multiply $x^{2}$ by $x$ by adding the exponents.

Tap for more steps...

Step 1.5.1.1

Multiply $x^{2}$ by $x$ .

Tap for more steps...

Step 1.5.1.1.1

Raise $x$ to the power of $1$ .

$\int_{0}^{10} x^{2} x^{1} + x^{2} (14 \sqrt{x}) + x^{2} \cdot 49 d x$

Step 1.5.1.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\int_{0}^{10} x^{2 + 1} + x^{2} (14 \sqrt{x}) + x^{2} \cdot 49 d x$

Step 1.5.1.2

Add $2$ and $1$ .

$\int_{0}^{10} x^{3} + x^{2} (14 \sqrt{x}) + x^{2} \cdot 49 d x$

Step 1.5.2

Rewrite using the commutative property of multiplication.

$\int_{0}^{10} x^{3} + 14 x^{2} \sqrt{x} + x^{2} \cdot 49 d x$

Step 1.5.3

Move $49$ to the left of $x^{2}$ .

$\int_{0}^{10} x^{3} + 14 x^{2} \sqrt{x} + 49 \cdot x^{2} d x$

$\int_{0}^{10} x^{3} + 14 x^{2} \sqrt{x} + 49 x^{2} d x$

Step 2

Simplify.

Tap for more steps...

Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

$\int_{0}^{10} x^{3} + 14 x^{2} x^{\frac{1}{2}} + 49 x^{2} d x$

Step 2.2

Multiply $x^{2}$ by $x^{\frac{1}{2}}$ by adding the exponents.

Tap for more steps...

Step 2.2.1

Move $x^{\frac{1}{2}}$ .

$\int_{0}^{10} x^{3} + 14 (x^{\frac{1}{2}} x^{2}) + 49 x^{2} d x$

Step 2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\int_{0}^{10} x^{3} + 14 x^{\frac{1}{2} + 2} + 49 x^{2} d x$

Step 2.2.3

To write $2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\int_{0}^{10} x^{3} + 14 x^{\frac{1}{2} + 2 \cdot \frac{2}{2}} + 49 x^{2} d x$

Step 2.2.4

Combine $2$ and $\frac{2}{2}$ .

$\int_{0}^{10} x^{3} + 14 x^{\frac{1}{2} + \frac{2 \cdot 2}{2}} + 49 x^{2} d x$

Step 2.2.5

Combine the numerators over the common denominator.

$\int_{0}^{10} x^{3} + 14 x^{\frac{1 + 2 \cdot 2}{2}} + 49 x^{2} d x$

Step 2.2.6

Simplify the numerator.

Tap for more steps...

Step 2.2.6.1

Multiply $2$ by $2$ .

$\int_{0}^{10} x^{3} + 14 x^{\frac{1 + 4}{2}} + 49 x^{2} d x$

Step 2.2.6.2

Add $1$ and $4$ .

$\int_{0}^{10} x^{3} + 14 x^{\frac{5}{2}} + 49 x^{2} d x$

Step 3

Split the single integral into multiple integrals.

$\int_{0}^{10} x^{3} d x + \int_{0}^{10} 14 x^{\frac{5}{2}} d x + \int_{0}^{10} 49 x^{2} d x$

Step 4

By the Power Rule, the integral of $x^{3}$ with respect to $x$ is $\frac{1}{4} x^{4}$ .

$\frac{1}{4} x^{4}]_{0}^{10} + \int_{0}^{10} 14 x^{\frac{5}{2}} d x + \int_{0}^{10} 49 x^{2} d x$

Step 5

Since $14$ is constant with respect to $x$ , move $14$ out of the integral.

$\frac{1}{4} x^{4}]_{0}^{10} + 14 \int_{0}^{10} x^{\frac{5}{2}} d x + \int_{0}^{10} 49 x^{2} d x$

Step 6

By the Power Rule, the integral of $x^{\frac{5}{2}}$ with respect to $x$ is $\frac{2}{7} x^{\frac{7}{2}}$ .

$\frac{1}{4} x^{4}]_{0}^{10} + 14 (\frac{2}{7} x^{\frac{7}{2}}]_{0}^{10}) + \int_{0}^{10} 49 x^{2} d x$

Step 7

Combine $\frac{2}{7}$ and $x^{\frac{7}{2}}$ .

$\frac{1}{4} x^{4}]_{0}^{10} + 14 (\frac{2 x^{\frac{7}{2}}}{7}]_{0}^{10}) + \int_{0}^{10} 49 x^{2} d x$

Step 8

Since $49$ is constant with respect to $x$ , move $49$ out of the integral.

$\frac{1}{4} x^{4}]_{0}^{10} + 14 (\frac{2 x^{\frac{7}{2}}}{7}]_{0}^{10}) + 49 \int_{0}^{10} x^{2} d x$

Step 9

By the Power Rule, the integral of $x^{2}$ with respect to $x$ is $\frac{1}{3} x^{3}$ .

$\frac{1}{4} x^{4}]_{0}^{10} + 14 (\frac{2 x^{\frac{7}{2}}}{7}]_{0}^{10}) + 49 (\frac{1}{3} x^{3}]_{0}^{10})$

Step 10

Simplify the answer.

Tap for more steps...

Step 10.1

Combine $\frac{1}{3}$ and $x^{3}$ .

$\frac{1}{4} x^{4}]_{0}^{10} + 14 (\frac{2 x^{\frac{7}{2}}}{7}]_{0}^{10}) + 49 (\frac{x^{3}}{3}]_{0}^{10})$

Step 10.2

Substitute and simplify.

Tap for more steps...

Step 10.2.1

Evaluate $\frac{1}{4} x^{4}$ at $10$ and at $0$ .

$(\frac{1}{4} \cdot 10^{4}) - \frac{1}{4} \cdot 0^{4} + 14 (\frac{2 x^{\frac{7}{2}}}{7}]_{0}^{10}) + 49 (\frac{x^{3}}{3}]_{0}^{10})$

Step 10.2.2

Evaluate $\frac{2 x^{\frac{7}{2}}}{7}$ at $10$ and at $0$ .

$\frac{1}{4} \cdot 10^{4} - \frac{1}{4} \cdot 0^{4} + 14 (\frac{2 \cdot 10^{\frac{7}{2}}}{7} - \frac{2 \cdot 0^{\frac{7}{2}}}{7}) + 49 (\frac{x^{3}}{3}]_{0}^{10})$

Step 10.2.3

Evaluate $\frac{x^{3}}{3}$ at $10$ and at $0$ .

$\frac{1}{4} \cdot 10^{4} - \frac{1}{4} \cdot 0^{4} + 14 (\frac{2 \cdot 10^{\frac{7}{2}}}{7} - \frac{2 \cdot 0^{\frac{7}{2}}}{7}) + 49 ((\frac{10^{3}}{3}) - \frac{0^{3}}{3})$

Step 10.2.4

Simplify.

Tap for more steps...

Step 10.2.4.1

Raise $10$ to the power of $4$ .

$\frac{1}{4} \cdot 10000 - \frac{1}{4} \cdot 0^{4} + 14 (\frac{2 \cdot 10^{\frac{7}{2}}}{7} - \frac{2 \cdot 0^{\frac{7}{2}}}{7}) + 49 ((\frac{10^{3}}{3}) - \frac{0^{3}}{3})$

Step 10.2.4.2

Combine $\frac{1}{4}$ and $10000$ .

$\frac{10000}{4} - \frac{1}{4} \cdot 0^{4} + 14 (\frac{2 \cdot 10^{\frac{7}{2}}}{7} - \frac{2 \cdot 0^{\frac{7}{2}}}{7}) + 49 ((\frac{10^{3}}{3}) - \frac{0^{3}}{3})$

Step 10.2.4.3

Cancel the common factor of $10000$ and $4$ .

Tap for more steps...

Step 10.2.4.3.1

Factor $4$ out of $10000$ .

$\frac{4 \cdot 2500}{4} - \frac{1}{4} \cdot 0^{4} + 14 (\frac{2 \cdot 10^{\frac{7}{2}}}{7} - \frac{2 \cdot 0^{\frac{7}{2}}}{7}) + 49 ((\frac{10^{3}}{3}) - \frac{0^{3}}{3})$

Step 10.2.4.3.2

Cancel the common factors.

Tap for more steps...

Step 10.2.4.3.2.1

Factor $4$ out of $4$ .

$\frac{4 \cdot 2500}{4 (1)} - \frac{1}{4} \cdot 0^{4} + 14 (\frac{2 \cdot 10^{\frac{7}{2}}}{7} - \frac{2 \cdot 0^{\frac{7}{2}}}{7}) + 49 ((\frac{10^{3}}{3}) - \frac{0^{3}}{3})$

Step 10.2.4.3.2.2

Cancel the common factor.

$\frac{4 \cdot 2500}{4 \cdot 1} - \frac{1}{4} \cdot 0^{4} + 14 (\frac{2 \cdot 10^{\frac{7}{2}}}{7} - \frac{2 \cdot 0^{\frac{7}{2}}}{7}) + 49 ((\frac{10^{3}}{3}) - \frac{0^{3}}{3})$

Step 10.2.4.3.2.3

Rewrite the expression.

$\frac{2500}{1} - \frac{1}{4} \cdot 0^{4} + 14 (\frac{2 \cdot 10^{\frac{7}{2}}}{7} - \frac{2 \cdot 0^{\frac{7}{2}}}{7}) + 49 ((\frac{10^{3}}{3}) - \frac{0^{3}}{3})$

Step 10.2.4.3.2.4

Divide $2500$ by $1$ .

$2500 - \frac{1}{4} \cdot 0^{4} + 14 (\frac{2 \cdot 10^{\frac{7}{2}}}{7} - \frac{2 \cdot 0^{\frac{7}{2}}}{7}) + 49 ((\frac{10^{3}}{3}) - \frac{0^{3}}{3})$

Step 10.2.4.4

Raising $0$ to any positive power yields $0$ .

$2500 - \frac{1}{4} \cdot 0 + 14 (\frac{2 \cdot 10^{\frac{7}{2}}}{7} - \frac{2 \cdot 0^{\frac{7}{2}}}{7}) + 49 ((\frac{10^{3}}{3}) - \frac{0^{3}}{3})$

Step 10.2.4.5

Multiply $0$ by $- 1$ .

$2500 + 0 (\frac{1}{4}) + 14 (\frac{2 \cdot 10^{\frac{7}{2}}}{7} - \frac{2 \cdot 0^{\frac{7}{2}}}{7}) + 49 ((\frac{10^{3}}{3}) - \frac{0^{3}}{3})$

Step 10.2.4.6

Multiply $0$ by $\frac{1}{4}$ .

$2500 + 0 + 14 (\frac{2 \cdot 10^{\frac{7}{2}}}{7} - \frac{2 \cdot 0^{\frac{7}{2}}}{7}) + 49 ((\frac{10^{3}}{3}) - \frac{0^{3}}{3})$

Step 10.2.4.7

Add $2500$ and $0$ .

$2500 + 14 (\frac{2 \cdot 10^{\frac{7}{2}}}{7} - \frac{2 \cdot 0^{\frac{7}{2}}}{7}) + 49 ((\frac{10^{3}}{3}) - \frac{0^{3}}{3})$

Step 10.2.4.8

Rewrite $0$ as $0^{2}$ .

$2500 + 14 (\frac{2 \cdot 10^{\frac{7}{2}}}{7} - \frac{2 \cdot {(0^{2})}^{\frac{7}{2}}}{7}) + 49 ((\frac{10^{3}}{3}) - \frac{0^{3}}{3})$

Step 10.2.4.9

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2500 + 14 (\frac{2 \cdot 10^{\frac{7}{2}}}{7} - \frac{2 \cdot 0^{2 (\frac{7}{2})}}{7}) + 49 ((\frac{10^{3}}{3}) - \frac{0^{3}}{3})$

Step 10.2.4.10

Cancel the common factor of $2$ .

Tap for more steps...

Step 10.2.4.10.1

Cancel the common factor.

$2500 + 14 (\frac{2 \cdot 10^{\frac{7}{2}}}{7} - \frac{2 \cdot 0^{2 (\frac{7}{2})}}{7}) + 49 ((\frac{10^{3}}{3}) - \frac{0^{3}}{3})$

Step 10.2.4.10.2

Rewrite the expression.

$2500 + 14 (\frac{2 \cdot 10^{\frac{7}{2}}}{7} - \frac{2 \cdot 0^{7}}{7}) + 49 ((\frac{10^{3}}{3}) - \frac{0^{3}}{3})$

Step 10.2.4.11

Raising $0$ to any positive power yields $0$ .

$2500 + 14 (\frac{2 \cdot 10^{\frac{7}{2}}}{7} - \frac{2 \cdot 0}{7}) + 49 ((\frac{10^{3}}{3}) - \frac{0^{3}}{3})$

Step 10.2.4.12

Multiply $2$ by $0$ .

$2500 + 14 (\frac{2 \cdot 10^{\frac{7}{2}}}{7} - \frac{0}{7}) + 49 ((\frac{10^{3}}{3}) - \frac{0^{3}}{3})$

Step 10.2.4.13

Cancel the common factor of $0$ and $7$ .

Tap for more steps...

Step 10.2.4.13.1

Factor $7$ out of $0$ .

$2500 + 14 (\frac{2 \cdot 10^{\frac{7}{2}}}{7} - \frac{7 (0)}{7}) + 49 ((\frac{10^{3}}{3}) - \frac{0^{3}}{3})$

Step 10.2.4.13.2

Cancel the common factors.

Tap for more steps...

Step 10.2.4.13.2.1

Factor $7$ out of $7$ .

$2500 + 14 (\frac{2 \cdot 10^{\frac{7}{2}}}{7} - \frac{7 \cdot 0}{7 \cdot 1}) + 49 ((\frac{10^{3}}{3}) - \frac{0^{3}}{3})$

Step 10.2.4.13.2.2

Cancel the common factor.

$2500 + 14 (\frac{2 \cdot 10^{\frac{7}{2}}}{7} - \frac{7 \cdot 0}{7 \cdot 1}) + 49 ((\frac{10^{3}}{3}) - \frac{0^{3}}{3})$

Step 10.2.4.13.2.3

Rewrite the expression.

$2500 + 14 (\frac{2 \cdot 10^{\frac{7}{2}}}{7} - \frac{0}{1}) + 49 ((\frac{10^{3}}{3}) - \frac{0^{3}}{3})$

Step 10.2.4.13.2.4

Divide $0$ by $1$ .

$2500 + 14 (\frac{2 \cdot 10^{\frac{7}{2}}}{7} - 0) + 49 ((\frac{10^{3}}{3}) - \frac{0^{3}}{3})$

Step 10.2.4.14

Multiply $- 1$ by $0$ .

$2500 + 14 (\frac{2 \cdot 10^{\frac{7}{2}}}{7} + 0) + 49 ((\frac{10^{3}}{3}) - \frac{0^{3}}{3})$

Step 10.2.4.15

Add $\frac{2 \cdot 10^{\frac{7}{2}}}{7}$ and $0$ .

$2500 + 14 \frac{2 \cdot 10^{\frac{7}{2}}}{7} + 49 ((\frac{10^{3}}{3}) - \frac{0^{3}}{3})$

Step 10.2.4.16

Combine $14$ and $\frac{2 \cdot 10^{\frac{7}{2}}}{7}$ .

$2500 + \frac{14 (2 \cdot 10^{\frac{7}{2}})}{7} + 49 ((\frac{10^{3}}{3}) - \frac{0^{3}}{3})$

Step 10.2.4.17

Multiply $2$ by $14$ .

$2500 + \frac{28 \cdot 10^{\frac{7}{2}}}{7} + 49 ((\frac{10^{3}}{3}) - \frac{0^{3}}{3})$

Step 10.2.4.18

Factor $7$ out of $28 \cdot 10^{\frac{7}{2}}$ .

$2500 + \frac{7 (4 \cdot 10^{\frac{7}{2}})}{7} + 49 ((\frac{10^{3}}{3}) - \frac{0^{3}}{3})$

Step 10.2.4.19

Cancel the common factors.

Tap for more steps...

Step 10.2.4.19.1

Factor $7$ out of $7$ .

$2500 + \frac{7 (4 \cdot 10^{\frac{7}{2}})}{7 (1)} + 49 ((\frac{10^{3}}{3}) - \frac{0^{3}}{3})$

Step 10.2.4.19.2

Cancel the common factor.

$2500 + \frac{7 (4 \cdot 10^{\frac{7}{2}})}{7 \cdot 1} + 49 ((\frac{10^{3}}{3}) - \frac{0^{3}}{3})$

Step 10.2.4.19.3

Rewrite the expression.

$2500 + \frac{4 \cdot 10^{\frac{7}{2}}}{1} + 49 ((\frac{10^{3}}{3}) - \frac{0^{3}}{3})$

Step 10.2.4.19.4

Divide $4 \cdot 10^{\frac{7}{2}}$ by $1$ .

$2500 + 4 \cdot 10^{\frac{7}{2}} + 49 ((\frac{10^{3}}{3}) - \frac{0^{3}}{3})$

Step 10.2.4.20

Raise $10$ to the power of $3$ .

$2500 + 4 \cdot 10^{\frac{7}{2}} + 49 (\frac{1000}{3} - \frac{0^{3}}{3})$

Step 10.2.4.21

Raising $0$ to any positive power yields $0$ .

$2500 + 4 \cdot 10^{\frac{7}{2}} + 49 (\frac{1000}{3} - \frac{0}{3})$

Step 10.2.4.22

Cancel the common factor of $0$ and $3$ .

Tap for more steps...

Step 10.2.4.22.1

Factor $3$ out of $0$ .

$2500 + 4 \cdot 10^{\frac{7}{2}} + 49 (\frac{1000}{3} - \frac{3 (0)}{3})$

Step 10.2.4.22.2

Cancel the common factors.

Tap for more steps...

Step 10.2.4.22.2.1

Factor $3$ out of $3$ .

$2500 + 4 \cdot 10^{\frac{7}{2}} + 49 (\frac{1000}{3} - \frac{3 \cdot 0}{3 \cdot 1})$

Step 10.2.4.22.2.2

Cancel the common factor.

$2500 + 4 \cdot 10^{\frac{7}{2}} + 49 (\frac{1000}{3} - \frac{3 \cdot 0}{3 \cdot 1})$

Step 10.2.4.22.2.3

Rewrite the expression.

$2500 + 4 \cdot 10^{\frac{7}{2}} + 49 (\frac{1000}{3} - \frac{0}{1})$

Step 10.2.4.22.2.4

Divide $0$ by $1$ .

$2500 + 4 \cdot 10^{\frac{7}{2}} + 49 (\frac{1000}{3} - 0)$

Step 10.2.4.23

Multiply $- 1$ by $0$ .

$2500 + 4 \cdot 10^{\frac{7}{2}} + 49 (\frac{1000}{3} + 0)$

Step 10.2.4.24

Add $\frac{1000}{3}$ and $0$ .

$2500 + 4 \cdot 10^{\frac{7}{2}} + 49 (\frac{1000}{3})$

Step 10.2.4.25

Combine $49$ and $\frac{1000}{3}$ .

$2500 + 4 \cdot 10^{\frac{7}{2}} + \frac{49 \cdot 1000}{3}$

Step 10.2.4.26

Multiply $49$ by $1000$ .

$2500 + 4 \cdot 10^{\frac{7}{2}} + \frac{49000}{3}$

Step 10.2.4.27

To write $2500$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$4 \cdot 10^{\frac{7}{2}} + 2500 \cdot \frac{3}{3} + \frac{49000}{3}$

Step 10.2.4.28

Combine $2500$ and $\frac{3}{3}$ .

$4 \cdot 10^{\frac{7}{2}} + \frac{2500 \cdot 3}{3} + \frac{49000}{3}$

Step 10.2.4.29

Combine the numerators over the common denominator.

$4 \cdot 10^{\frac{7}{2}} + \frac{2500 \cdot 3 + 49000}{3}$

Step 10.2.4.30

Simplify the numerator.

Tap for more steps...

Step 10.2.4.30.1

Multiply $2500$ by $3$ .

$4 \cdot 10^{\frac{7}{2}} + \frac{7500 + 49000}{3}$

Step 10.2.4.30.2

Add $7500$ and $49000$ .

$4 \cdot 10^{\frac{7}{2}} + \frac{56500}{3}$

Step 11

The result can be shown in multiple forms.

Scientific Notation:

$4 \cdot 10^{\frac{7}{2}} + \frac{56500}{3}$

Expanded Form:

$31482.443974$

Step 12