Algebra Examples

${(\frac{64}{81})}^{\frac{1}{2}}$

Step 1

Apply the product rule to $\frac{64}{81}$ .

$\frac{64^{\frac{1}{2}}}{81^{\frac{1}{2}}}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $64$ as $8^{2}$ .

$\frac{{(8^{2})}^{\frac{1}{2}}}{81^{\frac{1}{2}}}$

Step 2.2

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

$\frac{8^{2 (\frac{1}{2})}}{81^{\frac{1}{2}}}$

Step 2.3

Cancel the common factor of $2$ .

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Step 2.3.1

Cancel the common factor.

$\frac{8^{2 (\frac{1}{2})}}{81^{\frac{1}{2}}}$

Step 2.3.2

Rewrite the expression.

$\frac{8^{1}}{81^{\frac{1}{2}}}$

Step 2.4

Evaluate the exponent.

$\frac{8}{81^{\frac{1}{2}}}$

Step 3

Simplify the denominator.

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Step 3.1

Rewrite $81$ as $9^{2}$ .

$\frac{8}{{(9^{2})}^{\frac{1}{2}}}$

Step 3.2

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

$\frac{8}{9^{2 (\frac{1}{2})}}$

Step 3.3

Cancel the common factor of $2$ .

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Step 3.3.1

Cancel the common factor.

$\frac{8}{9^{2 (\frac{1}{2})}}$

Step 3.3.2

Rewrite the expression.

$\frac{8}{9^{1}}$

Step 3.4

Evaluate the exponent.

$\frac{8}{9}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{8}{9}$

Decimal Form:

$0.\overline{8}$