Solve ((2a^{2})^3)^2:(4a^2)^3+1

$$( ( 2 a ^ { 2 } ) ^ { 3 } ) ^ { 2 } : ( 4 a ^ { 2 } ) ^ { 3 } + 1$$

Evaluate

$$a^{6}+1$$

Solution Steps

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

$$\frac{\left(2a^{2}\right)^{6}}{\left(4a^{2}\right)^{3}}+1$$

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

$$\frac{2^{6}\left(a^{2}\right)^{6}}{\left(4a^{2}\right)^{3}}+1$$

To raise a power to another power, multiply the exponents. Multiply 2 and 6 to get 12.

$$\frac{2^{6}a^{12}}{\left(4a^{2}\right)^{3}}+1$$

Calculate 2 to the power of 6 and get 64.

$$\frac{64a^{12}}{\left(4a^{2}\right)^{3}}+1$$

Expand \left(4a^{2}\right)^{3}.

$$\frac{64a^{12}}{4^{3}\left(a^{2}\right)^{3}}+1$$

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

$$\frac{64a^{12}}{4^{3}a^{6}}+1$$

Calculate 4 to the power of 3 and get 64.

$$\frac{64a^{12}}{64a^{6}}+1$$

Cancel out 64a^{6} in both numerator and denominator.

$$a^{6}+1$$

Expand

$$a^{6}+1$$

Solution Steps

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

$$\frac{\left(2a^{2}\right)^{6}}{\left(4a^{2}\right)^{3}}+1$$

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

$$\frac{2^{6}\left(a^{2}\right)^{6}}{\left(4a^{2}\right)^{3}}+1$$

To raise a power to another power, multiply the exponents. Multiply 2 and 6 to get 12.

$$\frac{2^{6}a^{12}}{\left(4a^{2}\right)^{3}}+1$$

Calculate 2 to the power of 6 and get 64.

$$\frac{64a^{12}}{\left(4a^{2}\right)^{3}}+1$$

Expand \left(4a^{2}\right)^{3}.

$$\frac{64a^{12}}{4^{3}\left(a^{2}\right)^{3}}+1$$

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

$$\frac{64a^{12}}{4^{3}a^{6}}+1$$

Calculate 4 to the power of 3 and get 64.

$$\frac{64a^{12}}{64a^{6}}+1$$

Cancel out 64a^{6} in both numerator and denominator.

$$a^{6}+1$$