Simplify (1/4x^3y^-2)^-2(-4x^-1y)^-3

${(\frac{1}{4} x^{3} y^{- 2})}^{- 2} {(- 4 x^{- 1} y)}^{- 3}$

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

${(\frac{1}{4} \cdot (x^{3} \frac{1}{y^{2}}))}^{- 2} {(- 4 x^{- 1} y)}^{- 3}$

Combine $x^{3}$ and $\frac{1}{y^{2}}$ .

${(\frac{1}{4} \cdot \frac{x^{3}}{y^{2}})}^{- 2} {(- 4 x^{- 1} y)}^{- 3}$

Combine.

${(\frac{1 x^{3}}{4 y^{2}})}^{- 2} {(- 4 x^{- 1} y)}^{- 3}$

Multiply $x^{3}$ by $1$ .

${(\frac{x^{3}}{4 y^{2}})}^{- 2} {(- 4 x^{- 1} y)}^{- 3}$

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

${(\frac{4 y^{2}}{x^{3}})}^{2} {(- 4 x^{- 1} y)}^{- 3}$

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

Apply the product rule to $\frac{4 y^{2}}{x^{3}}$ .

$\frac{{(4 y^{2})}^{2}}{{(x^{3})}^{2}} {(- 4 x^{- 1} y)}^{- 3}$

Apply the product rule to $4 y^{2}$ .

$\frac{4^{2} {(y^{2})}^{2}}{{(x^{3})}^{2}} {(- 4 x^{- 1} y)}^{- 3}$

Simplify the numerator.

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

$\frac{16 {(y^{2})}^{2}}{{(x^{3})}^{2}} {(- 4 x^{- 1} y)}^{- 3}$

Multiply the exponents in ${(y^{2})}^{2}$ .

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

$\frac{16 y^{2 \cdot 2}}{{(x^{3})}^{2}} {(- 4 x^{- 1} y)}^{- 3}$

Multiply $2$ by $2$ .

$\frac{16 y^{4}}{{(x^{3})}^{2}} {(- 4 x^{- 1} y)}^{- 3}$

Multiply the exponents in ${(x^{3})}^{2}$ .

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

$\frac{16 y^{4}}{x^{3 \cdot 2}} {(- 4 x^{- 1} y)}^{- 3}$

Multiply $3$ by $2$ .

$\frac{16 y^{4}}{x^{6}} {(- 4 x^{- 1} y)}^{- 3}$

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

$\frac{16 y^{4}}{x^{6}} {(- 4 \frac{1}{x} y)}^{- 3}$

Combine $- 4$ and $\frac{1}{x}$ .

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

Move the negative in front of the fraction.

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

Combine $y$ and $\frac{4}{x}$ .

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

Move $4$ to the left of $y$ .

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

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

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

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

Apply the product rule to $- \frac{x}{4 y}$ .

$\frac{16 y^{4}}{x^{6}} ({(- 1)}^{3} {(\frac{x}{4 y})}^{3})$

Apply the product rule to $\frac{x}{4 y}$ .

$\frac{16 y^{4}}{x^{6}} ({(- 1)}^{3} \frac{x^{3}}{{(4 y)}^{3}})$

Apply the product rule to $4 y$ .

$\frac{16 y^{4}}{x^{6}} ({(- 1)}^{3} \frac{x^{3}}{4^{3} y^{3}})$

Simplify the expression.

Rewrite using the commutative property of multiplication.

${(- 1)}^{3} \frac{16 y^{4}}{x^{6}} \frac{x^{3}}{4^{3} y^{3}}$

Raise $- 1$ to the power of $3$ .

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

Cancel the common factor of $y^{3}$ .

Move the leading negative in $- \frac{16 y^{4}}{x^{6}}$ into the numerator.

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

Factor $y^{3}$ out of $- 16 y^{4}$ .

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

Factor $y^{3}$ out of $4^{3} y^{3}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x^{3}$ .

Factor $x^{3}$ out of $x^{6}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $\frac{- 16 y}{x^{3}}$ by $\frac{1}{4^{3}}$ .

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

Raise $4$ to the power of $3$ .

$\frac{- 16 y}{x^{3} \cdot 64}$

Cancel the common factor of $- 16$ and $64$ .

Factor $16$ out of $- 16 y$ .

$\frac{16 (- y)}{x^{3} \cdot 64}$

Cancel the common factors.

Factor $16$ out of $x^{3} \cdot 64$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{- y}{x^{3} \cdot 4}$

Simplify the expression.

Move $4$ to the left of $x^{3}$ .

$\frac{- y}{4 \cdot x^{3}}$

Move the negative in front of the fraction.

$- \frac{y}{4 x^{3}}$

Simplify (1/4x^3y^-2)^-2(-4x^-1y)^-3

Related Questions

Support LCMGCF.com by disabling your adblocker.