Solve (z^-2/2z^-6)^-3

$$( \frac { z ^ { - 2 } } { 2 z ^ { - 6 } } ) ^ { - 3 }$$

Evaluate

$$\frac{8}{z^{12}}$$

Solution Steps

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

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

To raise \frac{z^{4}}{2} to a power, raise both numerator and denominator to the power and then divide.

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

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

$$\frac{z^{-12}}{2^{-3}}$$

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

$$\frac{z^{-12}}{\frac{1}{8}}$$

Divide z^{-12} by \frac{1}{8} by multiplying z^{-12} by the reciprocal of \frac{1}{8}.

$$z^{-12}\times 8$$

Expand

$$\frac{8}{z^{12}}$$

Solution Steps

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

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

To raise \frac{z^{4}}{2} to a power, raise both numerator and denominator to the power and then divide.

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

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

$$\frac{z^{-12}}{2^{-3}}$$

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

$$\frac{z^{-12}}{\frac{1}{8}}$$

Divide z^{-12} by \frac{1}{8} by multiplying z^{-12} by the reciprocal of \frac{1}{8}.

$$z^{-12}\times 8$$