Evaluate 128^(-2/7)

$128^{- \frac{2}{7}}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{128^{\frac{2}{7}}}$

Step 2

Simplify the denominator.

Rewrite $128$ as $2^{7}$ .

$\frac{1}{{(2^{7})}^{\frac{2}{7}}}$

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

$\frac{1}{2^{7 (\frac{2}{7})}}$

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{1}{2^{7 (\frac{2}{7})}}$

Rewrite the expression.

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

Raise $2$ to the power of $2$ .

$\frac{1}{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{4}$

Decimal Form:

$0.25$