Solve frac{-4(m^{-3}z^4)^2}{12m^-4z^-1}

$$\frac { - 4 ( m ^ { - 3 } z ^ { 4 } ) ^ { 2 } } { 12 m ^ { - 4 } z ^ { - 1 } }$$

Evaluate

$$-\frac{z^{9}}{3m^{2}}$$

Solution Steps

Cancel out 4 in both numerator and denominator.

$$\frac{-\left(m^{-3}z^{4}\right)^{2}}{3m^{-4}\times \frac{1}{z}}$$

Expand \left(m^{-3}z^{4}\right)^{2}.

$$\frac{-\left(m^{-3}\right)^{2}\left(z^{4}\right)^{2}}{3m^{-4}\times \frac{1}{z}}$$

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

$$\frac{-m^{-6}\left(z^{4}\right)^{2}}{3m^{-4}\times \frac{1}{z}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{-m^{-6}z^{8}}{3m^{-4}\times \frac{1}{z}}$$

Express 3\times \frac{1}{z} as a single fraction.

$$\frac{-m^{-6}z^{8}}{\frac{3}{z}m^{-4}}$$

Express \frac{3}{z}m^{-4} as a single fraction.

$$\frac{-m^{-6}z^{8}}{\frac{3m^{-4}}{z}}$$

Divide -m^{-6}z^{8} by \frac{3m^{-4}}{z} by multiplying -m^{-6}z^{8} by the reciprocal of \frac{3m^{-4}}{z}.

$$\frac{-m^{-6}z^{8}z}{3m^{-4}}$$

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

$$\frac{-zz^{8}}{3m^{2}}$$

Cancel out -1 in both numerator and denominator.

$$\frac{zz^{8}}{-3m^{2}}$$

To multiply powers of the same base, add their exponents. Add 1 and 8 to get 9.

$$\frac{z^{9}}{-3m^{2}}$$

Expand

$$-\frac{z^{9}}{3m^{2}}$$

Solution Steps

Cancel out 4 in both numerator and denominator.

$$\frac{-\left(m^{-3}z^{4}\right)^{2}}{3m^{-4}\times \frac{1}{z}}$$

Expand \left(m^{-3}z^{4}\right)^{2}.

$$\frac{-\left(m^{-3}\right)^{2}\left(z^{4}\right)^{2}}{3m^{-4}\times \frac{1}{z}}$$

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

$$\frac{-m^{-6}\left(z^{4}\right)^{2}}{3m^{-4}\times \frac{1}{z}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{-m^{-6}z^{8}}{3m^{-4}\times \frac{1}{z}}$$

Express 3\times \frac{1}{z} as a single fraction.

$$\frac{-m^{-6}z^{8}}{\frac{3}{z}m^{-4}}$$

Express \frac{3}{z}m^{-4} as a single fraction.

$$\frac{-m^{-6}z^{8}}{\frac{3m^{-4}}{z}}$$

Divide -m^{-6}z^{8} by \frac{3m^{-4}}{z} by multiplying -m^{-6}z^{8} by the reciprocal of \frac{3m^{-4}}{z}.

$$\frac{-m^{-6}z^{8}z}{3m^{-4}}$$

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

$$\frac{-zz^{8}}{3m^{2}}$$

Cancel out -1 in both numerator and denominator.

$$\frac{zz^{8}}{-3m^{2}}$$

To multiply powers of the same base, add their exponents. Add 1 and 8 to get 9.

$$\frac{z^{9}}{-3m^{2}}$$