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

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

Evaluate

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

Solution Steps

Expand \left(z^{2}w^{-1}\right)^{3}.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

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

To raise a power to another power, multiply the exponents. Multiply -1 and 3 to get -3.

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

Expand \left(z^{3}w^{2}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

Cancel out z^{6} in both numerator and denominator.

$$\frac{w^{-3}}{w^{4}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

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

Expand

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

Solution Steps

Expand \left(z^{2}w^{-1}\right)^{3}.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

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

To raise a power to another power, multiply the exponents. Multiply -1 and 3 to get -3.

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

Expand \left(z^{3}w^{2}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

Cancel out z^{6} in both numerator and denominator.

$$\frac{w^{-3}}{w^{4}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

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