Solve (j^{2}k^{-1})^-3*(j^2/k^3)^-3

$$( j ^ { 2 } k ^ { - 1 } ) ^ { - 3 } \times ( \frac { j ^ { 2 } } { k ^ { 3 } } ) ^ { - 3 }$$

Evaluate

$$\left(\frac{k}{j}\right)^{12}$$

Solution Steps

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

$$\left(j^{2}\right)^{-3}\left(k^{-1}\right)^{-3}\times \left(\frac{j^{2}}{k^{3}}\right)^{-3}$$

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

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

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

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

To raise \frac{j^{2}}{k^{3}} to a power, raise both numerator and denominator to the power and then divide.

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

Express j^{-6}\times \frac{\left(j^{2}\right)^{-3}}{\left(k^{3}\right)^{-3}} as a single fraction.

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

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

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

To multiply powers of the same base, add their exponents. Add -6 and -6 to get -12.

$$\frac{j^{-12}}{\left(k^{3}\right)^{-3}}k^{3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -3 to get -9.

$$\frac{j^{-12}}{k^{-9}}k^{3}$$

Express \frac{j^{-12}}{k^{-9}}k^{3} as a single fraction.

$$\frac{j^{-12}k^{3}}{k^{-9}}$$

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

$$j^{-12}k^{12}$$

Expand

$$\left(\frac{k}{j}\right)^{12}$$

Solution Steps

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

$$\left(j^{2}\right)^{-3}\left(k^{-1}\right)^{-3}\times \left(\frac{j^{2}}{k^{3}}\right)^{-3}$$

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

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

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

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

To raise \frac{j^{2}}{k^{3}} to a power, raise both numerator and denominator to the power and then divide.

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

Express j^{-6}\times \frac{\left(j^{2}\right)^{-3}}{\left(k^{3}\right)^{-3}} as a single fraction.

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

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

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

To multiply powers of the same base, add their exponents. Add -6 and -6 to get -12.

$$\frac{j^{-12}}{\left(k^{3}\right)^{-3}}k^{3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -3 to get -9.

$$\frac{j^{-12}}{k^{-9}}k^{3}$$

Express \frac{j^{-12}}{k^{-9}}k^{3} as a single fraction.

$$\frac{j^{-12}k^{3}}{k^{-9}}$$

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

$$j^{-12}k^{12}$$