Solve left(-5xright)^2left(-2xright)^3-{left(1/2xright)}^2left(-2xright)^3

$${ \left(-5x \right) }^{ 2 } { \left(-2x \right) }^{ 3 } - { \left( \frac{ 1 }{ 2 } x \right) }^{ 2 } { \left(-2x \right) }^{ 3 }$$

Evaluate

$$-198x^{5}$$

Solution Steps

Expand \left(-5x\right)^{2}.

$$\left(-5\right)^{2}x^{2}\left(-2x\right)^{3}-\left(\frac{1}{2}x\right)^{2}\left(-2x\right)^{3}$$

Calculate -5 to the power of 2 and get 25.

$$25x^{2}\left(-2x\right)^{3}-\left(\frac{1}{2}x\right)^{2}\left(-2x\right)^{3}$$

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

$$25x^{2}\left(-2\right)^{3}x^{3}-\left(\frac{1}{2}x\right)^{2}\left(-2x\right)^{3}$$

Calculate -2 to the power of 3 and get -8.

$$25x^{2}\left(-8\right)x^{3}-\left(\frac{1}{2}x\right)^{2}\left(-2x\right)^{3}$$

Multiply 25 and -8 to get -200.

$$-200x^{2}x^{3}-\left(\frac{1}{2}x\right)^{2}\left(-2x\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$-200x^{5}-\left(\frac{1}{2}x\right)^{2}\left(-2x\right)^{3}$$

Expand \left(\frac{1}{2}x\right)^{2}.

$$-200x^{5}-\left(\frac{1}{2}\right)^{2}x^{2}\left(-2x\right)^{3}$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$-200x^{5}-\frac{1}{4}x^{2}\left(-2x\right)^{3}$$

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

$$-200x^{5}-\frac{1}{4}x^{2}\left(-2\right)^{3}x^{3}$$

Calculate -2 to the power of 3 and get -8.

$$-200x^{5}-\frac{1}{4}x^{2}\left(-8\right)x^{3}$$

Multiply \frac{1}{4} and -8 to get -2.

$$-200x^{5}-\left(-2x^{2}x^{3}\right)$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$-200x^{5}-\left(-2x^{5}\right)$$

The opposite of -2x^{5} is 2x^{5}.

$$-200x^{5}+2x^{5}$$

Combine -200x^{5} and 2x^{5} to get -198x^{5}.

$$-198x^{5}$$

Expand

$$-198x^{5}$$

Solution Steps

Expand \left(-5x\right)^{2}.

$$\left(-5\right)^{2}x^{2}\left(-2x\right)^{3}-\left(\frac{1}{2}x\right)^{2}\left(-2x\right)^{3}$$

Calculate -5 to the power of 2 and get 25.

$$25x^{2}\left(-2x\right)^{3}-\left(\frac{1}{2}x\right)^{2}\left(-2x\right)^{3}$$

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

$$25x^{2}\left(-2\right)^{3}x^{3}-\left(\frac{1}{2}x\right)^{2}\left(-2x\right)^{3}$$

Calculate -2 to the power of 3 and get -8.

$$25x^{2}\left(-8\right)x^{3}-\left(\frac{1}{2}x\right)^{2}\left(-2x\right)^{3}$$

Multiply 25 and -8 to get -200.

$$-200x^{2}x^{3}-\left(\frac{1}{2}x\right)^{2}\left(-2x\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$-200x^{5}-\left(\frac{1}{2}x\right)^{2}\left(-2x\right)^{3}$$

Expand \left(\frac{1}{2}x\right)^{2}.

$$-200x^{5}-\left(\frac{1}{2}\right)^{2}x^{2}\left(-2x\right)^{3}$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$-200x^{5}-\frac{1}{4}x^{2}\left(-2x\right)^{3}$$

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

$$-200x^{5}-\frac{1}{4}x^{2}\left(-2\right)^{3}x^{3}$$

Calculate -2 to the power of 3 and get -8.

$$-200x^{5}-\frac{1}{4}x^{2}\left(-8\right)x^{3}$$

Multiply \frac{1}{4} and -8 to get -2.

$$-200x^{5}-\left(-2x^{2}x^{3}\right)$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$-200x^{5}-\left(-2x^{5}\right)$$

The opposite of -2x^{5} is 2x^{5}.

$$-200x^{5}+2x^{5}$$

Combine -200x^{5} and 2x^{5} to get -198x^{5}.

$$-198x^{5}$$