Solve 10^-4=(10^-3)^2/c-10^-3

$$10 ^ { - 4 } = \frac { ( 10 ^ { - 3 } ) ^ { 2 } } { c - 10 ^ { - 3 } }$$

Solve for c

$$c=\frac{11}{1000}=0.011$$

Steps for Solving Linear Equation

To raise a power to another power, multiply the exponents. Multiply -3 and 2 to get -6.

$$10^{-4}=\frac{10^{-6}}{c-10^{-3}}$$

Calculate 10 to the power of -4 and get \frac{1}{10000}.

$$\frac{1}{10000}=\frac{10^{-6}}{c-10^{-3}}$$

Calculate 10 to the power of -6 and get \frac{1}{1000000}.

$$\frac{1}{10000}=\frac{\frac{1}{1000000}}{c-10^{-3}}$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\frac{1}{10000}=\frac{\frac{1}{1000000}}{c-\frac{1}{1000}}$$

Express \frac{\frac{1}{1000000}}{c-\frac{1}{1000}} as a single fraction.

$$\frac{1}{10000}=\frac{1}{1000000\left(c-\frac{1}{1000}\right)}$$

Use the distributive property to multiply 1000000 by c-\frac{1}{1000}.

$$\frac{1}{10000}=\frac{1}{1000000c-1000}$$

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

$$\frac{1}{1000000c-1000}=\frac{1}{10000}$$

Variable c cannot be equal to \frac{1}{1000} since division by zero is not defined. Multiply both sides of the equation by 10000\left(1000c-1\right), the least common multiple of 1000000c-1000,10000.

$$10=1000c-1$$

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

$$1000c-1=10$$

Add 1 to both sides.

$$1000c=10+1$$

Add 10 and 1 to get 11.

$$1000c=11$$

Divide both sides by 1000.

$$c=\frac{11}{1000}$$