Evaluate (256/625)^(-3/4)

${(\frac{256}{625})}^{- \frac{3}{4}}$

Step 1

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{625}{256})}^{\frac{3}{4}}$

Step 2

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

$\frac{625^{\frac{3}{4}}}{256^{\frac{3}{4}}}$

Step 3

Simplify the numerator.

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

$\frac{{(5^{4})}^{\frac{3}{4}}}{256^{\frac{3}{4}}}$

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

$\frac{5^{4 (\frac{3}{4})}}{256^{\frac{3}{4}}}$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{5^{4 (\frac{3}{4})}}{256^{\frac{3}{4}}}$

Rewrite the expression.

$\frac{5^{3}}{256^{\frac{3}{4}}}$

Raise $5$ to the power of $3$ .

$\frac{125}{256^{\frac{3}{4}}}$

Step 4

Simplify the denominator.

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

$\frac{125}{{(4^{4})}^{\frac{3}{4}}}$

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

$\frac{125}{4^{4 (\frac{3}{4})}}$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{125}{4^{4 (\frac{3}{4})}}$

Rewrite the expression.

$\frac{125}{4^{3}}$

Raise $4$ to the power of $3$ .

$\frac{125}{64}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{125}{64}$

Decimal Form:

$1.953125$

Mixed Number Form:

$1 \frac{61}{64}$