Solve (frac{k^{-4}*6k^2}{k^0*k^-3})^-3

$$( \frac { k ^ { - 4 } \cdot 6 k ^ { 2 } } { k ^ { 0 } \cdot k ^ { - 3 } } ) ^ { - 3 }$$

Evaluate

$$\frac{1}{216k^{3}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -4 and 2 to get -2.

$$\left(\frac{k^{-2}\times 6}{k^{0}k^{-3}}\right)^{-3}$$

To multiply powers of the same base, add their exponents. Add 0 and -3 to get -3.

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

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

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

Expand \left(6k^{1}\right)^{-3}.

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

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

$$6^{-3}k^{-3}$$

Calculate 6 to the power of -3 and get \frac{1}{216}.

$$\frac{1}{216}k^{-3}$$

Expand

$$\frac{1}{216k^{3}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -4 and 2 to get -2.

$$\left(\frac{k^{-2}\times 6}{k^{0}k^{-3}}\right)^{-3}$$

To multiply powers of the same base, add their exponents. Add 0 and -3 to get -3.

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

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

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

Expand \left(6k^{1}\right)^{-3}.

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

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

$$6^{-3}k^{-3}$$

Calculate 6 to the power of -3 and get \frac{1}{216}.

$$\frac{1}{216}k^{-3}$$