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

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

Evaluate

$$m^{3}$$

Solution Steps

Combine \frac{3}{2}m^{5} and -m^{5} to get \frac{1}{2}m^{5}.

$$\frac{\frac{1}{2}m^{5}}{m^{2}-\frac{1}{2}m^{2}}$$

Combine m^{2} and -\frac{1}{2}m^{2} to get \frac{1}{2}m^{2}.

$$\frac{\frac{1}{2}m^{5}}{\frac{1}{2}m^{2}}$$

Cancel out m^{2} in both numerator and denominator.

$$\frac{\frac{1}{2}m^{3}}{\frac{1}{2}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{m^{3}}{\left(\frac{1}{2}\right)^{0}}$$

Calculate \frac{1}{2} to the power of 0 and get 1.

$$\frac{m^{3}}{1}$$

Anything divided by one gives itself.

$$m^{3}$$

Expand

$$m^{3}$$

Solution Steps

Combine \frac{3}{2}m^{5} and -m^{5} to get \frac{1}{2}m^{5}.

$$\frac{\frac{1}{2}m^{5}}{m^{2}-\frac{1}{2}m^{2}}$$

Combine m^{2} and -\frac{1}{2}m^{2} to get \frac{1}{2}m^{2}.

$$\frac{\frac{1}{2}m^{5}}{\frac{1}{2}m^{2}}$$

Cancel out m^{2} in both numerator and denominator.

$$\frac{\frac{1}{2}m^{3}}{\frac{1}{2}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{m^{3}}{\left(\frac{1}{2}\right)^{0}}$$

Calculate \frac{1}{2} to the power of 0 and get 1.

$$\frac{m^{3}}{1}$$

Anything divided by one gives itself.

$$m^{3}$$