Basic Math Examples

\sqrt{2^{n}} = 32

$\sqrt{2^{n}} = 32$

Step 1

Use

\sqrt[n]{a^{x}} = a^{\frac{x}{n}}

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

\sqrt{2^{n}}

$\sqrt{2^{n}}$ as

2^{\frac{n}{2}}

$2^{\frac{n}{2}}$ .

2^{\frac{n}{2}} = 32

$2^{\frac{n}{2}} = 32$

Step 2

Create equivalent expressions in the equation that all have equal bases.

2^{\frac{n}{2}} = 2^{5}

$2^{\frac{n}{2}} = 2^{5}$

Step 3

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

\frac{n}{2} = 5

$\frac{n}{2} = 5$

Step 4

Solve for

n

$n$ .

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Step 4.1

Multiply both sides of the equation by

2

$2$ .

2 \frac{n}{2} = 2 \cdot 5

$2 \frac{n}{2} = 2 \cdot 5$

Step 4.2

Simplify both sides of the equation.

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Step 4.2.1

Simplify the left side.

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Step 4.2.1.1

Cancel the common factor of

2

$2$ .

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Step 4.2.1.1.1

Cancel the common factor.

$2 \frac{n}{2} = 2 \cdot 5$

Step 4.2.1.1.2

Rewrite the expression.

$n = 2 \cdot 5$

Step 4.2.2

Simplify the right side.

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Step 4.2.2.1

Multiply

$2$ by

$5$ .

$n = 10$