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

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

Evaluate

$$\frac{9}{m^{8}}$$

Solution Steps

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

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

To raise \frac{m^{4}}{3} to a power, raise both numerator and denominator to the power and then divide.

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

To raise a power to another power, multiply the exponents. Multiply 4 and -2 to get -8.

$$\frac{m^{-8}}{3^{-2}}$$

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

$$\frac{m^{-8}}{\frac{1}{9}}$$

Divide m^{-8} by \frac{1}{9} by multiplying m^{-8} by the reciprocal of \frac{1}{9}.

$$m^{-8}\times 9$$

Expand

$$\frac{9}{m^{8}}$$

Solution Steps

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

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

To raise \frac{m^{4}}{3} to a power, raise both numerator and denominator to the power and then divide.

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

To raise a power to another power, multiply the exponents. Multiply 4 and -2 to get -8.

$$\frac{m^{-8}}{3^{-2}}$$

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

$$\frac{m^{-8}}{\frac{1}{9}}$$

Divide m^{-8} by \frac{1}{9} by multiplying m^{-8} by the reciprocal of \frac{1}{9}.

$$m^{-8}\times 9$$