Solve (3p^3)^2/(2p^7)^3

$$\frac { ( 3 p ^ { 3 } ) ^ { 2 } } { ( 2 p ^ { 7 } ) ^ { 3 } }$$

Evaluate

$$\frac{9}{8p^{15}}$$

Solution Steps

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

$$\frac{3^{2}\left(p^{3}\right)^{2}}{\left(2p^{7}\right)^{3}}$$

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

$$\frac{3^{2}p^{6}}{\left(2p^{7}\right)^{3}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9p^{6}}{\left(2p^{7}\right)^{3}}$$

Expand \left(2p^{7}\right)^{3}.

$$\frac{9p^{6}}{2^{3}\left(p^{7}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 3 to get 21.

$$\frac{9p^{6}}{2^{3}p^{21}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{9p^{6}}{8p^{21}}$$

Cancel out p^{6} in both numerator and denominator.

$$\frac{9}{8p^{15}}$$

Expand

$$\frac{9}{8p^{15}}$$

Solution Steps

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

$$\frac{3^{2}\left(p^{3}\right)^{2}}{\left(2p^{7}\right)^{3}}$$

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

$$\frac{3^{2}p^{6}}{\left(2p^{7}\right)^{3}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9p^{6}}{\left(2p^{7}\right)^{3}}$$

Expand \left(2p^{7}\right)^{3}.

$$\frac{9p^{6}}{2^{3}\left(p^{7}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 3 to get 21.

$$\frac{9p^{6}}{2^{3}p^{21}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{9p^{6}}{8p^{21}}$$

Cancel out p^{6} in both numerator and denominator.

$$\frac{9}{8p^{15}}$$