Solve (2a^6)^4/(8a^5)^2

$$\frac { ( 2 a ^ { 6 } ) ^ { 4 } } { ( 8 a ^ { 5 } ) ^ { 2 } }$$

Evaluate

$$\frac{a^{14}}{4}$$

Solution Steps

Expand \left(2a^{6}\right)^{4}.

$$\frac{2^{4}\left(a^{6}\right)^{4}}{\left(8a^{5}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 4 to get 24.

$$\frac{2^{4}a^{24}}{\left(8a^{5}\right)^{2}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{16a^{24}}{\left(8a^{5}\right)^{2}}$$

Expand \left(8a^{5}\right)^{2}.

$$\frac{16a^{24}}{8^{2}\left(a^{5}\right)^{2}}$$

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

$$\frac{16a^{24}}{8^{2}a^{10}}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{16a^{24}}{64a^{10}}$$

Cancel out 16a^{10} in both numerator and denominator.

$$\frac{a^{14}}{4}$$

Expand

$$\frac{a^{14}}{4}$$

Solution Steps

Expand \left(2a^{6}\right)^{4}.

$$\frac{2^{4}\left(a^{6}\right)^{4}}{\left(8a^{5}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 4 to get 24.

$$\frac{2^{4}a^{24}}{\left(8a^{5}\right)^{2}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{16a^{24}}{\left(8a^{5}\right)^{2}}$$

Expand \left(8a^{5}\right)^{2}.

$$\frac{16a^{24}}{8^{2}\left(a^{5}\right)^{2}}$$

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

$$\frac{16a^{24}}{8^{2}a^{10}}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{16a^{24}}{64a^{10}}$$

Cancel out 16a^{10} in both numerator and denominator.

$$\frac{a^{14}}{4}$$