Simplify ((z^2w^-1)^3)/((z^3w^2)^2)

$\frac{{(z^{2} w^{- 1})}^{3}}{{(z^{3} w^{2})}^{2}}$

Step 1

Simplify the numerator.

Apply the product rule to $z^{2} w^{- 1}$ .

$\frac{{(z^{2})}^{3} {(w^{- 1})}^{3}}{{(z^{3} w^{2})}^{2}}$

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

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

$\frac{z^{2 \cdot 3} {(w^{- 1})}^{3}}{{(z^{3} w^{2})}^{2}}$

Multiply $2$ by $3$ .

$\frac{z^{6} {(w^{- 1})}^{3}}{{(z^{3} w^{2})}^{2}}$

Multiply the exponents in ${(w^{- 1})}^{3}$ .

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

$\frac{z^{6} w^{- 1 \cdot 3}}{{(z^{3} w^{2})}^{2}}$

Multiply $- 1$ by $3$ .

$\frac{z^{6} w^{- 3}}{{(z^{3} w^{2})}^{2}}$

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

$\frac{z^{6} \frac{1}{w^{3}}}{{(z^{3} w^{2})}^{2}}$

Step 2

Simplify the denominator.

Apply the product rule to $z^{3} w^{2}$ .

$\frac{z^{6} \frac{1}{w^{3}}}{{(z^{3})}^{2} {(w^{2})}^{2}}$

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

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

$\frac{z^{6} \frac{1}{w^{3}}}{z^{3 \cdot 2} {(w^{2})}^{2}}$

Multiply $3$ by $2$ .

$\frac{z^{6} \frac{1}{w^{3}}}{z^{6} {(w^{2})}^{2}}$

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

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

$\frac{z^{6} \frac{1}{w^{3}}}{z^{6} w^{2 \cdot 2}}$

Multiply $2$ by $2$ .

$\frac{z^{6} \frac{1}{w^{3}}}{z^{6} w^{4}}$

Step 3

Combine $z^{6}$ and $\frac{1}{w^{3}}$ .

$\frac{\frac{z^{6}}{w^{3}}}{z^{6} w^{4}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{z^{6}}{w^{3}} \cdot \frac{1}{z^{6} w^{4}}$

Step 5

Combine.

$\frac{z^{6} \cdot 1}{w^{3} (z^{6} w^{4})}$

Step 6

Multiply $w^{3}$ by $w^{4}$ by adding the exponents.

Move $w^{4}$ .

$\frac{z^{6} \cdot 1}{w^{4} w^{3} z^{6}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{z^{6} \cdot 1}{w^{4 + 3} z^{6}}$

Add $4$ and $3$ .

$\frac{z^{6} \cdot 1}{w^{7} z^{6}}$

Step 7

Multiply $z^{6}$ by $1$ .

$\frac{z^{6}}{w^{7} z^{6}}$

Step 8

Cancel the common factor of $z^{6}$ .

Cancel the common factor.

$\frac{z^{6}}{w^{7} z^{6}}$

Rewrite the expression.

$\frac{1}{w^{7}}$

Simplify ((z^2w^-1)^3)/((z^3w^2)^2)

Related Questions

Support LCMGCF.com by disabling your adblocker.