Solve (-3^{-1}h^{2}k^3)^2(-2h^4k)^-3

$$( - 3 ^ { - 1 } h ^ { 2 } k ^ { 3 } ) ^ { 2 } ( - 2 h ^ { 4 } k ) ^ { - 3 }$$

Evaluate

$$-\frac{k^{3}}{72h^{8}}$$

Solution Steps

Calculate 3 to the power of -1 and get \frac{1}{3}.

$$\left(-\frac{1}{3}h^{2}k^{3}\right)^{2}\left(-2h^{4}k\right)^{-3}$$

Expand \left(-\frac{1}{3}h^{2}k^{3}\right)^{2}.

$$\left(-\frac{1}{3}\right)^{2}\left(h^{2}\right)^{2}\left(k^{3}\right)^{2}\left(-2h^{4}k\right)^{-3}$$

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

$$\left(-\frac{1}{3}\right)^{2}h^{4}\left(k^{3}\right)^{2}\left(-2h^{4}k\right)^{-3}$$

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

$$\left(-\frac{1}{3}\right)^{2}h^{4}k^{6}\left(-2h^{4}k\right)^{-3}$$

Calculate -\frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{1}{9}h^{4}k^{6}\left(-2h^{4}k\right)^{-3}$$

Expand \left(-2h^{4}k\right)^{-3}.

$$\frac{1}{9}h^{4}k^{6}\left(-2\right)^{-3}\left(h^{4}\right)^{-3}k^{-3}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -3 to get -12.

$$\frac{1}{9}h^{4}k^{6}\left(-2\right)^{-3}h^{-12}k^{-3}$$

Calculate -2 to the power of -3 and get -\frac{1}{8}.

$$\frac{1}{9}h^{4}k^{6}\left(-\frac{1}{8}\right)h^{-12}k^{-3}$$

Multiply \frac{1}{9} and -\frac{1}{8} to get -\frac{1}{72}.

$$-\frac{1}{72}h^{4}k^{6}h^{-12}k^{-3}$$

To multiply powers of the same base, add their exponents. Add 4 and -12 to get -8.

$$-\frac{1}{72}h^{-8}k^{6}k^{-3}$$

To multiply powers of the same base, add their exponents. Add 6 and -3 to get 3.

$$-\frac{1}{72}h^{-8}k^{3}$$

Expand

$$-\frac{k^{3}}{72h^{8}}$$

Solution Steps

Calculate 3 to the power of -1 and get \frac{1}{3}.

$$\left(-\frac{1}{3}h^{2}k^{3}\right)^{2}\left(-2h^{4}k\right)^{-3}$$

Expand \left(-\frac{1}{3}h^{2}k^{3}\right)^{2}.

$$\left(-\frac{1}{3}\right)^{2}\left(h^{2}\right)^{2}\left(k^{3}\right)^{2}\left(-2h^{4}k\right)^{-3}$$

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

$$\left(-\frac{1}{3}\right)^{2}h^{4}\left(k^{3}\right)^{2}\left(-2h^{4}k\right)^{-3}$$

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

$$\left(-\frac{1}{3}\right)^{2}h^{4}k^{6}\left(-2h^{4}k\right)^{-3}$$

Calculate -\frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{1}{9}h^{4}k^{6}\left(-2h^{4}k\right)^{-3}$$

Expand \left(-2h^{4}k\right)^{-3}.

$$\frac{1}{9}h^{4}k^{6}\left(-2\right)^{-3}\left(h^{4}\right)^{-3}k^{-3}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -3 to get -12.

$$\frac{1}{9}h^{4}k^{6}\left(-2\right)^{-3}h^{-12}k^{-3}$$

Calculate -2 to the power of -3 and get -\frac{1}{8}.

$$\frac{1}{9}h^{4}k^{6}\left(-\frac{1}{8}\right)h^{-12}k^{-3}$$

Multiply \frac{1}{9} and -\frac{1}{8} to get -\frac{1}{72}.

$$-\frac{1}{72}h^{4}k^{6}h^{-12}k^{-3}$$

To multiply powers of the same base, add their exponents. Add 4 and -12 to get -8.

$$-\frac{1}{72}h^{-8}k^{6}k^{-3}$$

To multiply powers of the same base, add their exponents. Add 6 and -3 to get 3.

$$-\frac{1}{72}h^{-8}k^{3}$$