Solve (a^3)^2=(a^2)^3

$$( a ^ { 3 } ) ^ { 2 } = ( a ^ { 2 } ) ^ { 3 }$$

Solve for a (complex solution)

$$a\in \mathrm{C}$$

Solution Steps

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

$$a^{6}=\left(a^{2}\right)^{3}$$

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

$$a^{6}=a^{6}$$

Subtract a^{6} from both sides.

$$a^{6}-a^{6}=0$$

Combine a^{6} and -a^{6} to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any a.

$$a\in \mathrm{C}$$

Solve for a

$$a\in \mathrm{R}$$

Solution Steps

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

$$a^{6}=\left(a^{2}\right)^{3}$$

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

$$a^{6}=a^{6}$$

Subtract a^{6} from both sides.

$$a^{6}-a^{6}=0$$

Combine a^{6} and -a^{6} to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any a.

$$a\in \mathrm{R}$$