Solve left(2kright)^-3left(k^-5right)^-1/{left(6k^-2right)^1{left({k}^3right)}^-6}

$$\frac{ { \left(2k \right) }^{ -3 } { \left( { k }^{ -5 } \right) }^{ -1 } }{ { \left(6 { k }^{ -2 } \right) }^{ 1 } { \left( { k }^{ 3 } \right) }^{ -6 } }$$

Evaluate

$$\frac{k^{22}}{48}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -5 and -1 to get 5.

$$\frac{\left(2k\right)^{-3}k^{5}}{\left(6k^{-2}\right)^{1}\left(k^{3}\right)^{-6}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -6 to get -18.

$$\frac{\left(2k\right)^{-3}k^{5}}{\left(6k^{-2}\right)^{1}k^{-18}}$$

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

$$\frac{\left(2k\right)^{-3}k^{23}}{\left(6k^{-2}\right)^{1}}$$

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

$$\frac{2^{-3}k^{-3}k^{23}}{\left(6k^{-2}\right)^{1}}$$

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

$$\frac{\frac{1}{8}k^{-3}k^{23}}{\left(6k^{-2}\right)^{1}}$$

To multiply powers of the same base, add their exponents. Add -3 and 23 to get 20.

$$\frac{\frac{1}{8}k^{20}}{\left(6k^{-2}\right)^{1}}$$

Calculate 6k^{-2} to the power of 1 and get 6k^{-2}.

$$\frac{\frac{1}{8}k^{20}}{6k^{-2}}$$

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

$$\frac{\frac{1}{8}k^{22}}{6}$$

Divide \frac{1}{8}k^{22} by 6 to get \frac{1}{48}k^{22}.

$$\frac{1}{48}k^{22}$$

Expand

$$\frac{k^{22}}{48}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -5 and -1 to get 5.

$$\frac{\left(2k\right)^{-3}k^{5}}{\left(6k^{-2}\right)^{1}\left(k^{3}\right)^{-6}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -6 to get -18.

$$\frac{\left(2k\right)^{-3}k^{5}}{\left(6k^{-2}\right)^{1}k^{-18}}$$

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

$$\frac{\left(2k\right)^{-3}k^{23}}{\left(6k^{-2}\right)^{1}}$$

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

$$\frac{2^{-3}k^{-3}k^{23}}{\left(6k^{-2}\right)^{1}}$$

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

$$\frac{\frac{1}{8}k^{-3}k^{23}}{\left(6k^{-2}\right)^{1}}$$

To multiply powers of the same base, add their exponents. Add -3 and 23 to get 20.

$$\frac{\frac{1}{8}k^{20}}{\left(6k^{-2}\right)^{1}}$$

Calculate 6k^{-2} to the power of 1 and get 6k^{-2}.

$$\frac{\frac{1}{8}k^{20}}{6k^{-2}}$$

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

$$\frac{\frac{1}{8}k^{22}}{6}$$

Divide \frac{1}{8}k^{22} by 6 to get \frac{1}{48}k^{22}.

$$\frac{1}{48}k^{22}$$