How to Subtract Exponents

By Contributing Writer

An exponent, which is shorthand used to illustrate that a coefficient is repeatedly multiplied by itself, requires special consideration when performing algebra. The subtraction of two exponents is used to divide one exponential number or variable by the other as long as they have the same base.

Review that exponents are commonly used in algebra and represent the number of times the 'base', or the number represented by "x" in the expression of x^n, is multiplied by itself, represented by "n".

Remember the second law of exponents states that x^m / x^n = x^(m-n). When a number or variable that is in exponent notation is divided by another number or variable in the same base, the exponents are subtracted. If subtraction results in a negative exponent, the number is a fraction of 1.

Review the example of division between two exponential variables; divide the terms x^7 and x^3. This can be simplified and rewritten as x^7/x^3 or x^(7-3), which is equal to x^4.

Review the example of division between two exponential variables which cause a negative exponent; divide the terms x^5 and x^8. This can be simplified and rewritten as x^5/x^8 or x^(5-8), which is equal to x^(-3) or 1/x^3.

Practice algebra with variables in exponential form that also contain coefficients. For example; 15x^4 / 5x^2. The coefficients are divided as normal and the exponents are subtracted. The example can be simplified and rewritten as 15/5(x^(4-2)) which is equal to 3x^2.