Finite Math Examples

${(\sqrt{5 + 2})}^{48} {(\sqrt{5 - 2})}^{36}$

Step 1

Add $5$ and $2$ .

${\sqrt{7}}^{48} {(\sqrt{5 - 2})}^{36}$

Step 2

Rewrite ${\sqrt{7}}^{48}$ as $7^{24}$ .

Tap for more steps...

Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

${(7^{\frac{1}{2}})}^{48} {(\sqrt{5 - 2})}^{36}$

Step 2.2

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

$7^{\frac{1}{2} \cdot 48} {(\sqrt{5 - 2})}^{36}$

Step 2.3

Combine $\frac{1}{2}$ and $48$ .

$7^{\frac{48}{2}} {(\sqrt{5 - 2})}^{36}$

Step 2.4

Cancel the common factor of $48$ and $2$ .

Tap for more steps...

Step 2.4.1

Factor $2$ out of $48$ .

$7^{\frac{2 \cdot 24}{2}} {(\sqrt{5 - 2})}^{36}$

Step 2.4.2

Cancel the common factors.

Tap for more steps...

Step 2.4.2.1

Factor $2$ out of $2$ .

$7^{\frac{2 \cdot 24}{2 (1)}} {(\sqrt{5 - 2})}^{36}$

Step 2.4.2.2

Cancel the common factor.

$7^{\frac{2 \cdot 24}{2 \cdot 1}} {(\sqrt{5 - 2})}^{36}$

Step 2.4.2.3

Rewrite the expression.

$7^{\frac{24}{1}} {(\sqrt{5 - 2})}^{36}$

Step 2.4.2.4

Divide $24$ by $1$ .

$7^{24} {(\sqrt{5 - 2})}^{36}$

Step 3

Simplify the expression.

Tap for more steps...

Step 3.1

Raise $7$ to the power of $24$ .

$191581231380566000000 {(\sqrt{5 - 2})}^{36}$

Step 3.2

Subtract $2$ from $5$ .

$191581231380566000000 {\sqrt{3}}^{36}$

Step 4

Rewrite ${\sqrt{3}}^{36}$ as $3^{18}$ .

Tap for more steps...

Step 4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$191581231380566000000 {(3^{\frac{1}{2}})}^{36}$

Step 4.2

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

$191581231380566000000 \cdot 3^{\frac{1}{2} \cdot 36}$

Step 4.3

Combine $\frac{1}{2}$ and $36$ .

$191581231380566000000 \cdot 3^{\frac{36}{2}}$

Step 4.4

Cancel the common factor of $36$ and $2$ .

Tap for more steps...

Step 4.4.1

Factor $2$ out of $36$ .

$191581231380566000000 \cdot 3^{\frac{2 \cdot 18}{2}}$

Step 4.4.2

Cancel the common factors.

Tap for more steps...

Step 4.4.2.1

Factor $2$ out of $2$ .

$191581231380566000000 \cdot 3^{\frac{2 \cdot 18}{2 (1)}}$

Step 4.4.2.2

Cancel the common factor.

$191581231380566000000 \cdot 3^{\frac{2 \cdot 18}{2 \cdot 1}}$

Step 4.4.2.3

Rewrite the expression.

$191581231380566000000 \cdot 3^{\frac{18}{1}}$

Step 4.4.2.4

Divide $18$ by $1$ .

$191581231380566000000 \cdot 3^{18}$

Step 5

Simplify the expression.

Tap for more steps...

Step 5.1

Raise $3$ to the power of $18$ .

$191581231380566000000 \cdot 387420489$

Step 5.2

Multiply $191581231380566000000$ by $387420489$ .

$74222494344681024816774000000$

Step 6

The result can be shown in multiple forms.

Exact Form:

$74222494344681024816774000000$

Decimal Form:

$7.42224943 \cdot 10^{28}$