Simplify (-64/125)^(-2/3)

${(- \frac{64}{125})}^{\frac{- 2}{3}}$

Step 1

Move the negative in front of the fraction.

${(- \frac{64}{125})}^{- \frac{2}{3}}$

Step 2

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

${(- \frac{125}{64})}^{\frac{2}{3}}$

Step 3

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $- \frac{125}{64}$ .

${(- 1)}^{\frac{2}{3}} {(\frac{125}{64})}^{\frac{2}{3}}$

Apply the product rule to $\frac{125}{64}$ .

${(- 1)}^{\frac{2}{3}} \frac{125^{\frac{2}{3}}}{64^{\frac{2}{3}}}$

Step 4

Reduce the expression by cancelling the common factors.

Rewrite $- 1$ as ${(- 1)}^{3}$ .

${({(- 1)}^{3})}^{\frac{2}{3}} \frac{125^{\frac{2}{3}}}{64^{\frac{2}{3}}}$

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

${(- 1)}^{3 (\frac{2}{3})} \frac{125^{\frac{2}{3}}}{64^{\frac{2}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(- 1)}^{3 (\frac{2}{3})} \frac{125^{\frac{2}{3}}}{64^{\frac{2}{3}}}$

Rewrite the expression.

${(- 1)}^{2} \frac{125^{\frac{2}{3}}}{64^{\frac{2}{3}}}$

Simplify the expression.

Raise $- 1$ to the power of $2$ .

$1 \frac{125^{\frac{2}{3}}}{64^{\frac{2}{3}}}$

Multiply $\frac{125^{\frac{2}{3}}}{64^{\frac{2}{3}}}$ by $1$ .

$\frac{125^{\frac{2}{3}}}{64^{\frac{2}{3}}}$

Step 5

Simplify the numerator.

Rewrite $125$ as $5^{3}$ .

$\frac{{(5^{3})}^{\frac{2}{3}}}{64^{\frac{2}{3}}}$

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

$\frac{5^{3 (\frac{2}{3})}}{64^{\frac{2}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{5^{3 (\frac{2}{3})}}{64^{\frac{2}{3}}}$

Rewrite the expression.

$\frac{5^{2}}{64^{\frac{2}{3}}}$

Raise $5$ to the power of $2$ .

$\frac{25}{64^{\frac{2}{3}}}$

Step 6

Simplify the denominator.

Rewrite $64$ as $4^{3}$ .

$\frac{25}{{(4^{3})}^{\frac{2}{3}}}$

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

$\frac{25}{4^{3 (\frac{2}{3})}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{25}{4^{3 (\frac{2}{3})}}$

Rewrite the expression.

$\frac{25}{4^{2}}$

Raise $4$ to the power of $2$ .

$\frac{25}{16}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{25}{16}$

Decimal Form:

$1.5625$

Mixed Number Form:

$1 \frac{9}{16}$

Simplify (-64/125)^(-2/3)

Related Questions

Support LCMGCF.com by disabling your adblocker.