Simplify (64/81)^(1/2)

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

Step 1

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

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

Step 2

Simplify the numerator.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Step 3

Simplify the denominator.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

$\frac{8}{9}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{8}{9}$

Decimal Form:

$0.\overline{8}$