Solve (-5m)^2*(-2m)^3-(1/2m)^2*(-2m)^3

$$( - 5 m ) ^ { 2 } \times ( - 2 m ) ^ { 3 } - ( \frac { 1 } { 2 } m ) ^ { 2 } \times ( - 2 m ) ^ { 3 }$$

Evaluate

$$-198m^{5}$$

Solution Steps

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

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

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

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

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

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

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

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

Multiply 25 and -8 to get -200.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$-198m^{5}$$

Expand

$$-198m^{5}$$

Solution Steps

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

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

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

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

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

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

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

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

Multiply 25 and -8 to get -200.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$-198m^{5}$$