Solve (rs)^-5/(r^2s^3)^2=

$$\frac { ( r s ) ^ { - 5 } } { ( r ^ { 2 } s ^ { 3 } ) ^ { 2 } } =$$

Evaluate

$$\frac{1}{r^{9}s^{11}}$$

Solution Steps

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

$$\frac{r^{-5}s^{-5}}{\left(r^{2}s^{3}\right)^{2}}$$

Expand \left(r^{2}s^{3}\right)^{2}.

$$\frac{r^{-5}s^{-5}}{\left(r^{2}\right)^{2}\left(s^{3}\right)^{2}}$$

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

$$\frac{r^{-5}s^{-5}}{r^{4}\left(s^{3}\right)^{2}}$$

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

$$\frac{r^{-5}s^{-5}}{r^{4}s^{6}}$$

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

$$\frac{1}{r^{9}s^{11}}$$

Expand

$$\frac{1}{r^{9}s^{11}}$$

Solution Steps

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

$$\frac{r^{-5}s^{-5}}{\left(r^{2}s^{3}\right)^{2}}$$

Expand \left(r^{2}s^{3}\right)^{2}.

$$\frac{r^{-5}s^{-5}}{\left(r^{2}\right)^{2}\left(s^{3}\right)^{2}}$$

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

$$\frac{r^{-5}s^{-5}}{r^{4}\left(s^{3}\right)^{2}}$$

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

$$\frac{r^{-5}s^{-5}}{r^{4}s^{6}}$$

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

$$\frac{1}{r^{9}s^{11}}$$