Solve (-7x^3)^2-[(2x)^2]^3

$$( - 7 x ^ { 3 } ) ^ { 2 } - [ ( 2 x ) ^ { 2 } ] ^ { 3 }$$

Evaluate

$$-15x^{6}$$

Solution Steps

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

$$\left(-7x^{3}\right)^{2}-\left(2x\right)^{6}$$

Expand \left(-7x^{3}\right)^{2}.

$$\left(-7\right)^{2}\left(x^{3}\right)^{2}-\left(2x\right)^{6}$$

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

$$\left(-7\right)^{2}x^{6}-\left(2x\right)^{6}$$

Calculate -7 to the power of 2 and get 49.

$$49x^{6}-\left(2x\right)^{6}$$

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

$$49x^{6}-2^{6}x^{6}$$

Calculate 2 to the power of 6 and get 64.

$$49x^{6}-64x^{6}$$

Combine 49x^{6} and -64x^{6} to get -15x^{6}.

$$-15x^{6}$$

Expand

$$-15x^{6}$$

Solution Steps

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

$$\left(-7x^{3}\right)^{2}-\left(2x\right)^{6}$$

Expand \left(-7x^{3}\right)^{2}.

$$\left(-7\right)^{2}\left(x^{3}\right)^{2}-\left(2x\right)^{6}$$

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

$$\left(-7\right)^{2}x^{6}-\left(2x\right)^{6}$$

Calculate -7 to the power of 2 and get 49.

$$49x^{6}-\left(2x\right)^{6}$$

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

$$49x^{6}-2^{6}x^{6}$$

Calculate 2 to the power of 6 and get 64.

$$49x^{6}-64x^{6}$$

Combine 49x^{6} and -64x^{6} to get -15x^{6}.

$$-15x^{6}$$