Evaluate (256/625)^(1/4)

${(\frac{256}{625})}^{\frac{1}{4}}$

Step 1

Apply the product rule to $\frac{256}{625}$ .

$\frac{256^{\frac{1}{4}}}{625^{\frac{1}{4}}}$

Step 2

Simplify the numerator.

Rewrite $256$ as $4^{4}$ .

$\frac{{(4^{4})}^{\frac{1}{4}}}{625^{\frac{1}{4}}}$

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

$\frac{4^{4 (\frac{1}{4})}}{625^{\frac{1}{4}}}$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4^{4 (\frac{1}{4})}}{625^{\frac{1}{4}}}$

Rewrite the expression.

$\frac{4^{1}}{625^{\frac{1}{4}}}$

Evaluate the exponent.

$\frac{4}{625^{\frac{1}{4}}}$

Step 3

Simplify the denominator.

Rewrite $625$ as $5^{4}$ .

$\frac{4}{{(5^{4})}^{\frac{1}{4}}}$

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

$\frac{4}{5^{4 (\frac{1}{4})}}$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4}{5^{4 (\frac{1}{4})}}$

Rewrite the expression.

$\frac{4}{5^{1}}$

Evaluate the exponent.

$\frac{4}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{5}$

Decimal Form:

$0.8$