Finite Math Examples

$2 {(\sqrt{7})}^{10}$

Step 1

Rewrite ${\sqrt{7}}^{10}$ as $7^{5}$ .

Tap for more steps...

Step 1.1

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

$2 {(7^{\frac{1}{2}})}^{10}$

Step 1.2

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

$2 \cdot 7^{\frac{1}{2} \cdot 10}$

Step 1.3

Combine $\frac{1}{2}$ and $10$ .

$2 \cdot 7^{\frac{10}{2}}$

Step 1.4

Cancel the common factor of $10$ and $2$ .

Tap for more steps...

Step 1.4.1

Factor $2$ out of $10$ .

$2 \cdot 7^{\frac{2 \cdot 5}{2}}$

Step 1.4.2

Cancel the common factors.

Tap for more steps...

Step 1.4.2.1

Factor $2$ out of $2$ .

$2 \cdot 7^{\frac{2 \cdot 5}{2 (1)}}$

Step 1.4.2.2

Cancel the common factor.

$2 \cdot 7^{\frac{2 \cdot 5}{2 \cdot 1}}$

Step 1.4.2.3

Rewrite the expression.

$2 \cdot 7^{\frac{5}{1}}$

Step 1.4.2.4

Divide $5$ by $1$ .

$2 \cdot 7^{5}$

Step 2

Simplify the expression.

Tap for more steps...

Step 2.1

Raise $7$ to the power of $5$ .

$2 \cdot 16807$

Step 2.2

Multiply $2$ by $16807$ .

$33614$