# Rules That Cannot Be Overlooked While Multiplying Exponents

What are exponents and what are the rules for multiplying exponents? Here, we try to explain the rules for exponent multiplication to you.

Tulika Nair

Last Updated: Feb 26, 2019

^{3}. The rules for multiplying base numbers with exponents is slightly different from normal multiplication and here we try to explain those rules.

Multiplication Rules for Exponents

Multiplying Exponents of the Same Base Number

This is the rule for multiplying two exponents or powers that have the same base number. If this is the case, then all you need to do is keep the base number common and add the two exponents. The resultant exponent will be the new power for the base number. The exponential notation for this rule is:

**x**^{a}× x^{b}= x^{(a + b)}**2**

^{2}× 2^{3}= 2^{(2 + 3)}= 2^{5}= 32**Multiplying exponents when they have the same base is extremely simple as all you need to do is add the exponent powers together.**

Multiplying Exponents of Different Base Numbers

Multiplication rules for exponents of different base numbers is such that there is a shorter method of multiplication only if the exponent numbers are the same.

**x**

^{a}× y^{a}= (x × y)^{a}**(xy)**

^{a}= x^{a}× y^{a}**2**

^{2}× 3^{2}= (2 × 3)^{2}= 6^{2}= 36The process of multiplying different base numbers with the same exponential power is as easy as this.

Multiplying Exponent of an Exponent

Often you may be faced with a multiplication problem where the base number will have two exponent powers. In order to solve the power of a power, you will need to multiply the exponents together and then this would be the new exponent for the base number. This explanation will be made clear with the notational rule given below.

xx

^{(a)b}= x^{(a × b)}= x^{(ab)}**2**

^{(2)3}= 2^{(2 × 3)}= 2^{(6)}= 64**x**

^{a}÷ x^{b}= x^{(a)}(1/x^{b}) = x^{(a+ (-b))}= x^{(a -b)}**2**

^{5}÷ 2^{3}= 2^{(5)}(1/2^{3}) = 2^{(5+ (-3))}= x^{(5 -3)}= 2^{2}= 4