Algebra Examples

${(\frac{5^{4}}{3^{6}})}^{\frac{1}{2}}$

Step 1

Simplify the expression.

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Step 1.1

Raise $5$ to the power of $4$ .

${(\frac{625}{3^{6}})}^{\frac{1}{2}}$

Step 1.2

Raise $3$ to the power of $6$ .

${(\frac{625}{729})}^{\frac{1}{2}}$

Step 1.3

Apply the product rule to $\frac{625}{729}$ .

$\frac{625^{\frac{1}{2}}}{729^{\frac{1}{2}}}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $625$ as $25^{2}$ .

$\frac{{(25^{2})}^{\frac{1}{2}}}{729^{\frac{1}{2}}}$

Step 2.2

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

$\frac{25^{2 (\frac{1}{2})}}{729^{\frac{1}{2}}}$

Step 2.3

Cancel the common factor of $2$ .

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Step 2.3.1

Cancel the common factor.

$\frac{25^{2 (\frac{1}{2})}}{729^{\frac{1}{2}}}$

Step 2.3.2

Rewrite the expression.

$\frac{25^{1}}{729^{\frac{1}{2}}}$

Step 2.4

Evaluate the exponent.

$\frac{25}{729^{\frac{1}{2}}}$

Step 3

Simplify the denominator.

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Step 3.1

Rewrite $729$ as $27^{2}$ .

$\frac{25}{{(27^{2})}^{\frac{1}{2}}}$

Step 3.2

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

$\frac{25}{27^{2 (\frac{1}{2})}}$

Step 3.3

Cancel the common factor of $2$ .

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Step 3.3.1

Cancel the common factor.

$\frac{25}{27^{2 (\frac{1}{2})}}$

Step 3.3.2

Rewrite the expression.

$\frac{25}{27^{1}}$

Step 3.4

Evaluate the exponent.

$\frac{25}{27}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{25}{27}$

Decimal Form:

$0.\overline{925}$