Solve (frac{n^{-2}n^6}{3n^2n^-4})^-3

$$( \frac { n ^ { - 2 } n ^ { 6 } } { 3 n ^ { 2 } n ^ { - 4 } } ) ^ { - 3 }$$

Evaluate

$$\frac{27}{n^{18}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -2 and 6 to get 4.

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

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

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

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

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

To raise \frac{n^{6}}{3} to a power, raise both numerator and denominator to the power and then divide.

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

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

$$\frac{n^{-18}}{3^{-3}}$$

Calculate 3 to the power of -3 and get \frac{1}{27}.

$$\frac{n^{-18}}{\frac{1}{27}}$$

Divide n^{-18} by \frac{1}{27} by multiplying n^{-18} by the reciprocal of \frac{1}{27}.

$$n^{-18}\times 27$$

Expand

$$\frac{27}{n^{18}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -2 and 6 to get 4.

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

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

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

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

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

To raise \frac{n^{6}}{3} to a power, raise both numerator and denominator to the power and then divide.

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

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

$$\frac{n^{-18}}{3^{-3}}$$

Calculate 3 to the power of -3 and get \frac{1}{27}.

$$\frac{n^{-18}}{\frac{1}{27}}$$

Divide n^{-18} by \frac{1}{27} by multiplying n^{-18} by the reciprocal of \frac{1}{27}.

$$n^{-18}\times 27$$