Solve (4a^5)^2/(3a^7)^3

$$\frac { ( 4 a ^ { 5 } ) ^ { 2 } } { ( 3 a ^ { 7 } ) ^ { 3 } }$$

Evaluate

$$\frac{16}{27a^{11}}$$

Solution Steps

Expand \left(4a^{5}\right)^{2}.

$$\frac{4^{2}\left(a^{5}\right)^{2}}{\left(3a^{7}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{4^{2}a^{10}}{\left(3a^{7}\right)^{3}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{16a^{10}}{\left(3a^{7}\right)^{3}}$$

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

$$\frac{16a^{10}}{3^{3}\left(a^{7}\right)^{3}}$$

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

$$\frac{16a^{10}}{3^{3}a^{21}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{16a^{10}}{27a^{21}}$$

Cancel out a^{10} in both numerator and denominator.

$$\frac{16}{27a^{11}}$$

Expand

$$\frac{16}{27a^{11}}$$

Solution Steps

Expand \left(4a^{5}\right)^{2}.

$$\frac{4^{2}\left(a^{5}\right)^{2}}{\left(3a^{7}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{4^{2}a^{10}}{\left(3a^{7}\right)^{3}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{16a^{10}}{\left(3a^{7}\right)^{3}}$$

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

$$\frac{16a^{10}}{3^{3}\left(a^{7}\right)^{3}}$$

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

$$\frac{16a^{10}}{3^{3}a^{21}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{16a^{10}}{27a^{21}}$$

Cancel out a^{10} in both numerator and denominator.

$$\frac{16}{27a^{11}}$$