How to Add and Subtract Exponents & Powers

Exponents are a shorthand tool in math.

Exponents are an abbreviated way to show a number multiplied by itself a certain number of times. For example, instead of writing out g*g*g*g*g*g*g, you would simply write g^7. The first number in the expression is the base and in g^7, "g" would be the base. The number after the caret (^) is the power, so in g^7, "7" would be the power. You cannot add or subtract exponents. For example, you could not simplify x^4 + x^3. If exponents are being multiplied or divided, however, you can simplify them by adding or subtracting the powers.

Things You'll Need

• Calculator

Instructions

1. Identify the exponents that have like bases in the expression. For example, if you had the expression (x^6 * x^5 * y^3) / x^3, you would be able to simplify the (x^6 * x^5) / x^3, but you could not simplify the y^3 term because it has a different base.

2. Add the powers of the exponents that have like bases and are being multiplied. For example, in the expression (x^6 * x^5 * y^3) / x^3, you would see that x^6 and x^5 have the same base and are being multiplied, so you would add 6 and 5 to get 11. You would simplify the expression to (x^11 * y^3) / x^3.

3. Subtract powers of the exponents that have like bases and are being divided. Continuing the example, in the expression (x^11 * y^3) / x^3, you would see that x^11 is being divided by x^3 so you would subtract 3 from 11 to get 8. Therefore, the expression would be simplified to x^8 * y^3.

4. Stop when you have no more like bases. In the expression x^8 * y^3, you cannot simplify any further because the bases are not the same.

References

• West Texas A&M: Exponents
• SOS Math: Exponential Rules