Solve (2x^2)^3-(2x^3)^2

$$( 2 x ^ { 2 } ) ^ { 3 } - ( 2 x ^ { 3 } ) ^ { 2 }$$

Evaluate

$$4x^{6}$$

Solution Steps

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

$$2^{3}\left(x^{2}\right)^{3}-\left(2x^{3}\right)^{2}$$

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

$$2^{3}x^{6}-\left(2x^{3}\right)^{2}$$

Calculate 2 to the power of 3 and get 8.

$$8x^{6}-\left(2x^{3}\right)^{2}$$

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

$$8x^{6}-2^{2}\left(x^{3}\right)^{2}$$

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

$$8x^{6}-2^{2}x^{6}$$

Calculate 2 to the power of 2 and get 4.

$$8x^{6}-4x^{6}$$

Combine 8x^{6} and -4x^{6} to get 4x^{6}.

$$4x^{6}$$

Expand

$$4x^{6}$$

Solution Steps

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

$$2^{3}\left(x^{2}\right)^{3}-\left(2x^{3}\right)^{2}$$

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

$$2^{3}x^{6}-\left(2x^{3}\right)^{2}$$

Calculate 2 to the power of 3 and get 8.

$$8x^{6}-\left(2x^{3}\right)^{2}$$

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

$$8x^{6}-2^{2}\left(x^{3}\right)^{2}$$

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

$$8x^{6}-2^{2}x^{6}$$

Calculate 2 to the power of 2 and get 4.

$$8x^{6}-4x^{6}$$

Combine 8x^{6} and -4x^{6} to get 4x^{6}.

$$4x^{6}$$