Basic Math Examples

${(\sqrt{v + 7})}^{2} = 3^{2}$

Step 1

Rewrite ${\sqrt{v + 7}}^{2}$ as $v + 7$ .

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Step 1.1

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

${({(v + 7)}^{\frac{1}{2}})}^{2} = 3^{2}$

Step 1.2

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

${(v + 7)}^{\frac{1}{2} \cdot 2} = 3^{2}$

Step 1.3

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

${(v + 7)}^{\frac{2}{2}} = 3^{2}$

Step 1.4

Cancel the common factor of $2$ .

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Step 1.4.1

Cancel the common factor.

${(v + 7)}^{\frac{2}{2}} = 3^{2}$

Step 1.4.2

Rewrite the expression.

${(v + 7)}^{1} = 3^{2}$

Step 1.5

Simplify.

$v + 7 = 3^{2}$

Step 2

Raise $3$ to the power of $2$ .

$v + 7 = 9$

Step 3

Move all terms not containing $v$ to the right side of the equation.

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Step 3.1

Subtract $7$ from both sides of the equation.

$v = 9 - 7$

Step 3.2

Subtract $7$ from $9$ .

$v = 2$