Simplify -(27/(64y^6))^(2/3)

$- {(\frac{27}{64 y^{6}})}^{\frac{2}{3}}$

Step 1

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

Apply the product rule to $\frac{27}{64 y^{6}}$ .

$- \frac{27^{\frac{2}{3}}}{{(64 y^{6})}^{\frac{2}{3}}}$

Apply the product rule to $64 y^{6}$ .

$- \frac{27^{\frac{2}{3}}}{64^{\frac{2}{3}} {(y^{6})}^{\frac{2}{3}}}$

Step 2

Simplify the numerator.

Rewrite $27$ as $3^{3}$ .

$- \frac{{(3^{3})}^{\frac{2}{3}}}{64^{\frac{2}{3}} {(y^{6})}^{\frac{2}{3}}}$

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

$- \frac{3^{3 (\frac{2}{3})}}{64^{\frac{2}{3}} {(y^{6})}^{\frac{2}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$- \frac{3^{3 (\frac{2}{3})}}{64^{\frac{2}{3}} {(y^{6})}^{\frac{2}{3}}}$

Rewrite the expression.

$- \frac{3^{2}}{64^{\frac{2}{3}} {(y^{6})}^{\frac{2}{3}}}$

Raise $3$ to the power of $2$ .

$- \frac{9}{64^{\frac{2}{3}} {(y^{6})}^{\frac{2}{3}}}$

Step 3

Simplify the denominator.

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

$- \frac{9}{{(4^{3})}^{\frac{2}{3}} {(y^{6})}^{\frac{2}{3}}}$

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

$- \frac{9}{4^{3 (\frac{2}{3})} {(y^{6})}^{\frac{2}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$- \frac{9}{4^{3 (\frac{2}{3})} {(y^{6})}^{\frac{2}{3}}}$

Rewrite the expression.

$- \frac{9}{4^{2} {(y^{6})}^{\frac{2}{3}}}$

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

$- \frac{9}{16 {(y^{6})}^{\frac{2}{3}}}$

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

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

$- \frac{9}{16 y^{6 (\frac{2}{3})}}$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$- \frac{9}{16 y^{3 (2) \frac{2}{3}}}$

Cancel the common factor.

$- \frac{9}{16 y^{3 \cdot 2 \frac{2}{3}}}$

Rewrite the expression.

$- \frac{9}{16 y^{2 \cdot 2}}$

Multiply $2$ by $2$ .

$- \frac{9}{16 y^{4}}$