Solve frac{(x^{2}*y^{-3}*z^-2)^2}{x^4*y^8}

$$\frac { ( x ^ { 2 } \cdot y ^ { - 3 } \cdot z ^ { - 2 } ) ^ { 2 } } { x ^ { 4 } \cdot y ^ { 8 } }$$

Evaluate

$$\frac{1}{z^{4}y^{14}}$$

Solution Steps

Expand \left(x^{2}y^{-3}z^{-2}\right)^{2}.

$$\frac{\left(x^{2}\right)^{2}\left(y^{-3}\right)^{2}\left(z^{-2}\right)^{2}}{x^{4}y^{8}}$$

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

$$\frac{x^{4}\left(y^{-3}\right)^{2}\left(z^{-2}\right)^{2}}{x^{4}y^{8}}$$

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

$$\frac{x^{4}y^{-6}\left(z^{-2}\right)^{2}}{x^{4}y^{8}}$$

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

$$\frac{x^{4}y^{-6}z^{-4}}{x^{4}y^{8}}$$

Cancel out x^{4} in both numerator and denominator.

$$\frac{y^{-6}z^{-4}}{y^{8}}$$

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

$$\frac{z^{-4}}{y^{14}}$$

Expand

$$\frac{1}{z^{4}y^{14}}$$

Solution Steps

Expand \left(x^{2}y^{-3}z^{-2}\right)^{2}.

$$\frac{\left(x^{2}\right)^{2}\left(y^{-3}\right)^{2}\left(z^{-2}\right)^{2}}{x^{4}y^{8}}$$

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

$$\frac{x^{4}\left(y^{-3}\right)^{2}\left(z^{-2}\right)^{2}}{x^{4}y^{8}}$$

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

$$\frac{x^{4}y^{-6}\left(z^{-2}\right)^{2}}{x^{4}y^{8}}$$

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

$$\frac{x^{4}y^{-6}z^{-4}}{x^{4}y^{8}}$$

Cancel out x^{4} in both numerator and denominator.

$$\frac{y^{-6}z^{-4}}{y^{8}}$$

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

$$\frac{z^{-4}}{y^{14}}$$