Solve 5y^4n^-4/(3n^-5)^-3

$$\frac { 5 y ^ { 4 } n ^ { - 4 } } { ( 3 n ^ { - 5 } ) ^ { - 3 } }$$

Evaluate

$$\frac{135y^{4}}{n^{19}}$$

Solution Steps

Expand \left(3n^{-5}\right)^{-3}.

$$\frac{5y^{4}n^{-4}}{3^{-3}\left(n^{-5}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply -5 and -3 to get 15.

$$\frac{5y^{4}n^{-4}}{3^{-3}n^{15}}$$

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

$$\frac{5y^{4}n^{-4}}{\frac{1}{27}n^{15}}$$

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

$$\frac{5y^{4}}{\frac{1}{27}n^{19}}$$

Expand

$$\frac{135y^{4}}{n^{19}}$$

Solution Steps

Expand \left(3n^{-5}\right)^{-3}.

$$\frac{5y^{4}n^{-4}}{3^{-3}\left(n^{-5}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply -5 and -3 to get 15.

$$\frac{5y^{4}n^{-4}}{3^{-3}n^{15}}$$

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

$$\frac{5y^{4}n^{-4}}{\frac{1}{27}n^{15}}$$

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

$$\frac{5y^{4}}{\frac{1}{27}n^{19}}$$