Solve frac{27r^{9}*s^15}{(3r^2s^5)^4}

$$\frac { 27 r ^ { 9 } \cdot s ^ { 15 } } { ( 3 r ^ { 2 } s ^ { 5 } ) ^ { 4 } }$$

Evaluate

$$\frac{r}{3s^{5}}$$

Solution Steps

Expand \left(3r^{2}s^{5}\right)^{4}.

$$\frac{27r^{9}s^{15}}{3^{4}\left(r^{2}\right)^{4}\left(s^{5}\right)^{4}}$$

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

$$\frac{27r^{9}s^{15}}{3^{4}r^{8}\left(s^{5}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 4 to get 20.

$$\frac{27r^{9}s^{15}}{3^{4}r^{8}s^{20}}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{27r^{9}s^{15}}{81r^{8}s^{20}}$$

Cancel out 27r^{8}s^{15} in both numerator and denominator.

$$\frac{r}{3s^{5}}$$

Expand

$$\frac{r}{3s^{5}}$$

Solution Steps

Expand \left(3r^{2}s^{5}\right)^{4}.

$$\frac{27r^{9}s^{15}}{3^{4}\left(r^{2}\right)^{4}\left(s^{5}\right)^{4}}$$

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

$$\frac{27r^{9}s^{15}}{3^{4}r^{8}\left(s^{5}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 4 to get 20.

$$\frac{27r^{9}s^{15}}{3^{4}r^{8}s^{20}}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{27r^{9}s^{15}}{81r^{8}s^{20}}$$

Cancel out 27r^{8}s^{15} in both numerator and denominator.

$$\frac{r}{3s^{5}}$$