 Geometry - Properties of exponents

Exponent of a number (number is called base) tells how many times the number is to be multiplied. For eg. 8 power 3 (written as 8^3) means 8 is to be multiplied three times. The property of negative exponents is as follows : it tells us “how many times to divide one by the number”. For example, 8^(-4) = 1/8^4. Any exponent to the zero power is equal to one except when the base is 0 (i.e. 0^0 is indeterminate). There are few rules of exponents (also called laws of exponents or properties of exponents) which include fractions as exponents, multiplying exponents etc. one should be familiar with, for simplifying expressions with exponents. Learn more about these rules by using the resources on this page.

Related Topics

• Can you subtract exponents with the same base?

• Adding and Subtracting Quantities with Exponents. We cannot simplify by grouping two terms together unless they have the same base and the same exponent. For example, we cannot combine terms in expressions such as 52 +122 or 53 +54 . We can, however, simplify 45 +45 and 2x 2 +5x 2 .

• Can you add numbers with exponents?

• To add or subtract with powers, both the variables and the exponents of the variables must be the same. You perform the required operations on the coefficients, leaving the variable and exponent as they are.

• What is the product property of exponents?

• The product of powers rule states that when multiplying two powers with the same base, just add the exponents.

• Why do you subtract the exponents when dividing powers of the same base?

• To divide exponents (or powers) with the same base, subtract the exponents. Division is the opposite of multiplication, so it makes sense that because you add exponents when multiplying numbers with the same base, you subtract the exponents when dividing numbers with the same base.

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