Simplify (16x^-8y^-16)^(-3/4)

${(16 x^{- 8} y^{- 16})}^{- \frac{3}{4}}$

Step 1

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

${(16 \frac{1}{x^{8}} y^{- 16})}^{- \frac{3}{4}}$

Step 2

Combine $16$ and $\frac{1}{x^{8}}$ .

${(\frac{16}{x^{8}} y^{- 16})}^{- \frac{3}{4}}$

Step 3

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

${(\frac{16}{x^{8}} \cdot \frac{1}{y^{16}})}^{- \frac{3}{4}}$

Step 4

Combine.

${(\frac{16 \cdot 1}{x^{8} y^{16}})}^{- \frac{3}{4}}$

Step 5

Multiply $16$ by $1$ .

${(\frac{16}{x^{8} y^{16}})}^{- \frac{3}{4}}$

Step 6

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

${(\frac{x^{8} y^{16}}{16})}^{\frac{3}{4}}$

Step 7

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

Apply the product rule to $\frac{x^{8} y^{16}}{16}$ .

$\frac{{(x^{8} y^{16})}^{\frac{3}{4}}}{16^{\frac{3}{4}}}$

Apply the product rule to $x^{8} y^{16}$ .

$\frac{{(x^{8})}^{\frac{3}{4}} {(y^{16})}^{\frac{3}{4}}}{16^{\frac{3}{4}}}$

Step 8

Simplify the numerator.

Multiply the exponents in ${(x^{8})}^{\frac{3}{4}}$ .

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

$\frac{x^{8 (\frac{3}{4})} {(y^{16})}^{\frac{3}{4}}}{16^{\frac{3}{4}}}$

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$\frac{x^{4 (2) \frac{3}{4}} {(y^{16})}^{\frac{3}{4}}}{16^{\frac{3}{4}}}$

Cancel the common factor.

$\frac{x^{4 \cdot 2 \frac{3}{4}} {(y^{16})}^{\frac{3}{4}}}{16^{\frac{3}{4}}}$

Rewrite the expression.

$\frac{x^{2 \cdot 3} {(y^{16})}^{\frac{3}{4}}}{16^{\frac{3}{4}}}$

Multiply $2$ by $3$ .

$\frac{x^{6} {(y^{16})}^{\frac{3}{4}}}{16^{\frac{3}{4}}}$

Multiply the exponents in ${(y^{16})}^{\frac{3}{4}}$ .

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

$\frac{x^{6} y^{16 (\frac{3}{4})}}{16^{\frac{3}{4}}}$

Cancel the common factor of $4$ .

Factor $4$ out of $16$ .

$\frac{x^{6} y^{4 (4) \frac{3}{4}}}{16^{\frac{3}{4}}}$

Cancel the common factor.

$\frac{x^{6} y^{4 \cdot 4 \frac{3}{4}}}{16^{\frac{3}{4}}}$

Rewrite the expression.

$\frac{x^{6} y^{4 \cdot 3}}{16^{\frac{3}{4}}}$

Multiply $4$ by $3$ .

$\frac{x^{6} y^{12}}{16^{\frac{3}{4}}}$

Step 9

Simplify the denominator.

Rewrite $16$ as $2^{4}$ .

$\frac{x^{6} y^{12}}{{(2^{4})}^{\frac{3}{4}}}$

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

$\frac{x^{6} y^{12}}{2^{4 (\frac{3}{4})}}$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{x^{6} y^{12}}{2^{4 (\frac{3}{4})}}$

Rewrite the expression.

$\frac{x^{6} y^{12}}{2^{3}}$

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

$\frac{x^{6} y^{12}}{8}$

Simplify (16x^-8y^-16)^(-3/4)

Related Questions

Support LCMGCF.com by disabling your adblocker.