What is an Exponent

Publish date: 2024-06-16

What is an Exponent Definition:

Shorthand for how many times
a number or variable
is multiplied by itself.

Why use exponents:

Represent large numbers or small numbers.

Integers raised to a positive exponent:

2 times itself 3 times, 2 * 2 * 2
We can use exponents as follows:
23 where 2 is the base and 3 is the exponent

Both of these expressions equal each other
23 = 2 * 2 * 2

Variables raised to a positive exponent:

x times itself 3 times, x * x * x
We can use exponents as follows:
x3 where x is the base and 3 is the exponent

Both of these expressions equal each other
x3 = x * x * x

Product Rule for Exponents:

Given a number a with exponents m and n:
am * an = am + n

Product Rule for Exponents Example:

Let a = 5 with exponents m = 4 and n = 3:
54 * 53 = 54 + 3
54 * 53 = 57
625 * 125 ? 78125
78,125 = 78,125

Quotient Rule for Exponents:

Given a number a with exponents m and n:

am - n =	am
	an

Quotient Rule for Exponents Example:

Let a = 5 with exponents m = 4 and n = 3:

54 - 3 =	54
	53

51 =	625
	125

5 = 5

Power of a Power Rule for Exponents:

Given a number a with exponents m and n:
(am)n = amn

Power of a Power Rule for Exponents Example:

Let a = 5 with exponents m = 4 and n = 3:
(54)3 = 54 * 3
6253 = 512
244,140,625 = 244,140,625

Power of a Product Rule for Exponents:

Given a number a and a number b with exponent n:
(ab)n = anbn

Power of a Product Rule for Exponents Example:

Let a = 4 and b = 3 and n = 5:
(4 * 3)5 = 4535
125 = 1024 * 243
248832 = 248832

Power of a Quotient Rule for Exponents:

Given a number a and a number b with exponent n:
(a/b)n = an/bn

Power of a Quotient Rule for Exponents Example:

Let a = 4 and b = 3 and n = 5:
(4/3)5 = 45/35
(1.3333333333333)5 = 1024/243
4.21399176955 = 4.21399176955

Negative Integer Exponent Rule:

Given a number a with exponent -n:
a-n = (1/a)n

Zero Exponent Rule:

Given a number a with exponent 0, any we have:
a0 = 1
Anything raised to the 0 power = 1

How does the What is an Exponent Calculator work?

Free What is an Exponent Calculator - This lesson walks you through what an exponent is, the product rule for exponents, the quotient rule for exponents, the 0 power rule, the power of a power rule for exponents

What 5 formulas are used for the What is an Exponent Calculator?

mxa + nxa = (m + n)xa
mxa - nxa = (m - n)xa
(xm)n = xm * n
xm * xn = xm + n
xm/xn = xm - n

For more math formulas, check out our Formula Dossier

What 7 concepts are covered in the What is an Exponent Calculator?

additionmath operation involving the sum of elementsexponentThe power to raise a numbermultiplicationmath operation involving the product of elementspowerhow many times to use the number in a multiplicationproductThe answer when two or more values are multiplied togetherquotientThe result of dividing two expressions.subtractionmath operation involving the difference of elements