Solve (x+h/10)=(-2m^{2}n^-1)^2*m^-3n^3

$$( x + \frac { h } { 10 } ) = ( - 2 m ^ { 2 } n ^ { - 1 } ) ^ { 2 } \cdot m ^ { - 3 } n ^ { 3 }$$

Solve for h

$$h=40mn-10x$$

$$n\neq 0\text{ and }m\neq 0$$

Solution Steps

Multiply both sides of the equation by 10.

$$10x+h=10\left(-2m^{2}n^{-1}\right)^{2}m^{-3}n^{3}$$

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

$$10x+h=10\left(-2\right)^{2}\left(m^{2}\right)^{2}\left(n^{-1}\right)^{2}m^{-3}n^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$10x+h=10\left(-2\right)^{2}m^{4}\left(n^{-1}\right)^{2}m^{-3}n^{3}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.

$$10x+h=10\left(-2\right)^{2}m^{4}n^{-2}m^{-3}n^{3}$$

Calculate -2 to the power of 2 and get 4.

$$10x+h=10\times 4m^{4}n^{-2}m^{-3}n^{3}$$

Multiply 10 and 4 to get 40.

$$10x+h=40m^{4}n^{-2}m^{-3}n^{3}$$

To multiply powers of the same base, add their exponents. Add 4 and -3 to get 1.

$$10x+h=40m^{1}n^{-2}n^{3}$$

To multiply powers of the same base, add their exponents. Add -2 and 3 to get 1.

$$10x+h=40m^{1}n^{1}$$

Calculate m to the power of 1 and get m.

$$10x+h=40mn^{1}$$

Calculate n to the power of 1 and get n.

$$10x+h=40mn$$

Subtract 10x from both sides.

$$h=40mn-10x$$

Solve for m

$$m=\frac{10x+h}{40n}$$

$$n\neq 0\text{ and }x\neq -\frac{h}{10}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 10.

$$10x+h=10\left(-2m^{2}n^{-1}\right)^{2}m^{-3}n^{3}$$

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

$$10x+h=10\left(-2\right)^{2}\left(m^{2}\right)^{2}\left(n^{-1}\right)^{2}m^{-3}n^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$10x+h=10\left(-2\right)^{2}m^{4}\left(n^{-1}\right)^{2}m^{-3}n^{3}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.

$$10x+h=10\left(-2\right)^{2}m^{4}n^{-2}m^{-3}n^{3}$$

Calculate -2 to the power of 2 and get 4.

$$10x+h=10\times 4m^{4}n^{-2}m^{-3}n^{3}$$

Multiply 10 and 4 to get 40.

$$10x+h=40m^{4}n^{-2}m^{-3}n^{3}$$

To multiply powers of the same base, add their exponents. Add 4 and -3 to get 1.

$$10x+h=40m^{1}n^{-2}n^{3}$$

To multiply powers of the same base, add their exponents. Add -2 and 3 to get 1.

$$10x+h=40m^{1}n^{1}$$

Calculate m to the power of 1 and get m.

$$10x+h=40mn^{1}$$

Calculate n to the power of 1 and get n.

$$10x+h=40mn$$

Swap sides so that all variable terms are on the left hand side.

$$40mn=10x+h$$

The equation is in standard form.

$$40nm=10x+h$$

Divide both sides by 40n.

$$\frac{40nm}{40n}=\frac{10x+h}{40n}$$

Dividing by 40n undoes the multiplication by 40n.

$$m=\frac{10x+h}{40n}$$