Solve 21/2m^2n+31/3m^2n-frac{2}1^-3m^2n

$$2 \frac { 1 } { 2 } m ^ { 2 } n + 3 \frac { 1 } { 3 } m ^ { 2 } n - \frac { 2 } { 1 } ^ { - 3 } m ^ { 2 } n$$

Evaluate

$$\frac{137nm^{2}}{24}$$

Solution Steps

Multiply 2 and 2 to get 4.

$$\frac{4+1}{2}m^{2}n+\frac{3\times 3+1}{3}m^{2}n-\left(\frac{2}{1}\right)^{-3}m^{2}n$$

Add 4 and 1 to get 5.

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

Multiply 3 and 3 to get 9.

$$\frac{5}{2}m^{2}n+\frac{9+1}{3}m^{2}n-\left(\frac{2}{1}\right)^{-3}m^{2}n$$

Add 9 and 1 to get 10.

$$\frac{5}{2}m^{2}n+\frac{10}{3}m^{2}n-\left(\frac{2}{1}\right)^{-3}m^{2}n$$

Combine \frac{5}{2}m^{2}n and \frac{10}{3}m^{2}n to get \frac{35}{6}m^{2}n.

$$\frac{35}{6}m^{2}n-\left(\frac{2}{1}\right)^{-3}m^{2}n$$

Anything divided by one gives itself.

$$\frac{35}{6}m^{2}n-2^{-3}m^{2}n$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$\frac{35}{6}m^{2}n-\frac{1}{8}m^{2}n$$

Combine \frac{35}{6}m^{2}n and -\frac{1}{8}m^{2}n to get \frac{137}{24}m^{2}n.

$$\frac{137}{24}m^{2}n$$

Expand

$$\frac{137nm^{2}}{24}$$

Solution Steps

Multiply 2 and 2 to get 4.

$$\frac{4+1}{2}m^{2}n+\frac{3\times 3+1}{3}m^{2}n-\left(\frac{2}{1}\right)^{-3}m^{2}n$$

Add 4 and 1 to get 5.

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

Multiply 3 and 3 to get 9.

$$\frac{5}{2}m^{2}n+\frac{9+1}{3}m^{2}n-\left(\frac{2}{1}\right)^{-3}m^{2}n$$

Add 9 and 1 to get 10.

$$\frac{5}{2}m^{2}n+\frac{10}{3}m^{2}n-\left(\frac{2}{1}\right)^{-3}m^{2}n$$

Combine \frac{5}{2}m^{2}n and \frac{10}{3}m^{2}n to get \frac{35}{6}m^{2}n.

$$\frac{35}{6}m^{2}n-\left(\frac{2}{1}\right)^{-3}m^{2}n$$

Anything divided by one gives itself.

$$\frac{35}{6}m^{2}n-2^{-3}m^{2}n$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$\frac{35}{6}m^{2}n-\frac{1}{8}m^{2}n$$

Combine \frac{35}{6}m^{2}n and -\frac{1}{8}m^{2}n to get \frac{137}{24}m^{2}n.

$$\frac{137}{24}m^{2}n$$