Basic Math Examples

$\frac{1}{2} \cdot \frac{4}{3} \cdot 3.14 \cdot {7.5}^{3} + 3.14 \cdot {7.5}^{2} \cdot 7.5$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $2$ .

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Step 1.1.1

Factor $2$ out of $4$ .

$\frac{1}{2} \cdot \frac{2 (2)}{3} \cdot 3.14 \cdot {7.5}^{3} + 3.14 \cdot {7.5}^{2} \cdot 7.5$

Step 1.1.2

Cancel the common factor.

$\frac{1}{2} \cdot \frac{2 \cdot 2}{3} \cdot 3.14 \cdot {7.5}^{3} + 3.14 \cdot {7.5}^{2} \cdot 7.5$

Step 1.1.3

Rewrite the expression.

$\frac{2}{3} \cdot 3.14 \cdot {7.5}^{3} + 3.14 \cdot {7.5}^{2} \cdot 7.5$

Step 1.2

Multiply $\frac{2}{3} \cdot 3.14$ .

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Step 1.2.1

Combine $\frac{2}{3}$ and $3.14$ .

$\frac{2 \cdot 3.14}{3} \cdot {7.5}^{3} + 3.14 \cdot {7.5}^{2} \cdot 7.5$

Step 1.2.2

Multiply $2$ by $3.14$ .

$\frac{6.28}{3} \cdot {7.5}^{3} + 3.14 \cdot {7.5}^{2} \cdot 7.5$

Step 1.3

Divide $6.28$ by $3$ .

$2.09\overline{3} \cdot {7.5}^{3} + 3.14 \cdot {7.5}^{2} \cdot 7.5$

Step 1.4

Raise $7.5$ to the power of $3$ .

$2.09\overline{3} \cdot 421.875 + 3.14 \cdot {7.5}^{2} \cdot 7.5$

Step 1.5

Multiply $2.09\overline{3}$ by $421.875$ .

$883.125 + 3.14 \cdot {7.5}^{2} \cdot 7.5$

Step 1.6

Multiply ${7.5}^{2}$ by $7.5$ by adding the exponents.

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Step 1.6.1

Move $7.5$ .

$883.125 + 3.14 \cdot (7.5 \cdot {7.5}^{2})$

Step 1.6.2

Multiply $7.5$ by ${7.5}^{2}$ .

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Step 1.6.2.1

Raise $7.5$ to the power of $1$ .

$883.125 + 3.14 \cdot ({7.5}^{1} \cdot {7.5}^{2})$

Step 1.6.2.2

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

$883.125 + 3.14 \cdot {7.5}^{1 + 2}$

Step 1.6.3

Add $1$ and $2$ .

$883.125 + 3.14 \cdot {7.5}^{3}$

Step 1.7

Raise $7.5$ to the power of $3$ .

$883.125 + 3.14 \cdot 421.875$

Step 1.8

Multiply $3.14$ by $421.875$ .

$883.125 + 1324.6875$

Step 2

Add $883.125$ and $1324.6875$ .

$2207.8125$