Basic Math Examples

$\sqrt[5]{25^{a}} = 5$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{25^{a}}$ as $25^{\frac{a}{5}}$ .

$25^{\frac{a}{5}} = 5$

Step 2

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

$5^{2 \frac{a}{5}} = 5^{1}$

Step 3

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

$2 \frac{a}{5} = 1$

Step 4

Solve for $a$ .

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Step 4.1

Combine $2$ and $\frac{a}{5}$ .

$\frac{2 a}{5} = 1$

Step 4.2

Multiply both sides of the equation by $\frac{5}{2}$ .

$\frac{5}{2} \cdot \frac{2 a}{5} = \frac{5}{2} \cdot 1$

Step 4.3

Simplify both sides of the equation.

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Step 4.3.1

Simplify the left side.

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Step 4.3.1.1

Simplify $\frac{5}{2} \cdot \frac{2 a}{5}$ .

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Step 4.3.1.1.1

Cancel the common factor of $5$ .

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Step 4.3.1.1.1.1

Cancel the common factor.

$\frac{5}{2} \cdot \frac{2 a}{5} = \frac{5}{2} \cdot 1$

Step 4.3.1.1.1.2

Rewrite the expression.

$\frac{1}{2} (2 a) = \frac{5}{2} \cdot 1$

Step 4.3.1.1.2

Cancel the common factor of $2$ .

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Step 4.3.1.1.2.1

Factor $2$ out of $2 a$ .

$\frac{1}{2} (2 (a)) = \frac{5}{2} \cdot 1$

Step 4.3.1.1.2.2

Cancel the common factor.

$\frac{1}{2} (2 a) = \frac{5}{2} \cdot 1$

Step 4.3.1.1.2.3

Rewrite the expression.

$a = \frac{5}{2} \cdot 1$

Step 4.3.2

Simplify the right side.

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Step 4.3.2.1

Multiply $\frac{5}{2}$ by $1$ .

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$a = 2.5$

Mixed Number Form:

$a = 2 \frac{1}{2}$