Simplify ((125a^3)/(8b^6))^(-2/3)

${(\frac{125 a^{3}}{8 b^{6}})}^{- \frac{2}{3}}$

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

${(\frac{8 b^{6}}{125 a^{3}})}^{\frac{2}{3}}$

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

Apply the product rule to $\frac{8 b^{6}}{125 a^{3}}$ .

$\frac{{(8 b^{6})}^{\frac{2}{3}}}{{(125 a^{3})}^{\frac{2}{3}}}$

Apply the product rule to $8 b^{6}$ .

$\frac{8^{\frac{2}{3}} {(b^{6})}^{\frac{2}{3}}}{{(125 a^{3})}^{\frac{2}{3}}}$

Apply the product rule to $125 a^{3}$ .

$\frac{8^{\frac{2}{3}} {(b^{6})}^{\frac{2}{3}}}{125^{\frac{2}{3}} {(a^{3})}^{\frac{2}{3}}}$

Simplify the numerator.

Rewrite $8$ as $2^{3}$ .

$\frac{{(2^{3})}^{\frac{2}{3}} {(b^{6})}^{\frac{2}{3}}}{125^{\frac{2}{3}} {(a^{3})}^{\frac{2}{3}}}$

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

$\frac{2^{3 (\frac{2}{3})} {(b^{6})}^{\frac{2}{3}}}{125^{\frac{2}{3}} {(a^{3})}^{\frac{2}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{2^{3 (\frac{2}{3})} {(b^{6})}^{\frac{2}{3}}}{125^{\frac{2}{3}} {(a^{3})}^{\frac{2}{3}}}$

Rewrite the expression.

$\frac{2^{2} {(b^{6})}^{\frac{2}{3}}}{125^{\frac{2}{3}} {(a^{3})}^{\frac{2}{3}}}$

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

$\frac{4 {(b^{6})}^{\frac{2}{3}}}{125^{\frac{2}{3}} {(a^{3})}^{\frac{2}{3}}}$

Multiply the exponents in ${(b^{6})}^{\frac{2}{3}}$ .

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

$\frac{4 b^{6 (\frac{2}{3})}}{125^{\frac{2}{3}} {(a^{3})}^{\frac{2}{3}}}$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$\frac{4 b^{3 (2) \frac{2}{3}}}{125^{\frac{2}{3}} {(a^{3})}^{\frac{2}{3}}}$

Cancel the common factor.

$\frac{4 b^{3 \cdot 2 \frac{2}{3}}}{125^{\frac{2}{3}} {(a^{3})}^{\frac{2}{3}}}$

Rewrite the expression.

$\frac{4 b^{2 \cdot 2}}{125^{\frac{2}{3}} {(a^{3})}^{\frac{2}{3}}}$

Multiply $2$ by $2$ .

$\frac{4 b^{4}}{125^{\frac{2}{3}} {(a^{3})}^{\frac{2}{3}}}$

Simplify the denominator.

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

$\frac{4 b^{4}}{{(5^{3})}^{\frac{2}{3}} {(a^{3})}^{\frac{2}{3}}}$

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

$\frac{4 b^{4}}{5^{3 (\frac{2}{3})} {(a^{3})}^{\frac{2}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{4 b^{4}}{5^{3 (\frac{2}{3})} {(a^{3})}^{\frac{2}{3}}}$

Rewrite the expression.

$\frac{4 b^{4}}{5^{2} {(a^{3})}^{\frac{2}{3}}}$

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

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

Multiply the exponents in ${(a^{3})}^{\frac{2}{3}}$ .

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify ((125a^3)/(8b^6))^(-2/3)

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