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

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

Evaluate

$$\frac{a^{12}}{4}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$\frac{2^{4}a^{16}}{\left(8a^{2}\right)^{2}}$$

Calculate 2 to the power of 4 and get 16.

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

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

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

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

$$\frac{16a^{16}}{8^{2}a^{4}}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{16a^{16}}{64a^{4}}$$

Cancel out 16a^{4} in both numerator and denominator.

$$\frac{a^{12}}{4}$$

Expand

$$\frac{a^{12}}{4}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$\frac{2^{4}a^{16}}{\left(8a^{2}\right)^{2}}$$

Calculate 2 to the power of 4 and get 16.

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

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

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

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

$$\frac{16a^{16}}{8^{2}a^{4}}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{16a^{16}}{64a^{4}}$$

Cancel out 16a^{4} in both numerator and denominator.

$$\frac{a^{12}}{4}$$