Master The Math Of Division Property Of Exponents: Simplify Powers With The Same Base

division property of exponents

a^x/a^y = a^x-y

The division property of exponents states that when dividing two powers with the same base, we can subtract their exponents to get the resulting power. In other words, if we have two non-zero numbers a and b, and x and y are any real numbers, then:

a^x / a^y = a^(x-y)
and
b^x / b^y = b^(x-y)

For example, let’s suppose that we want to divide the following powers with the same base:

2^5 / 2^3

Using the division property of exponents, we can subtract their exponents to obtain the result as follows:

2^5 / 2^3 = 2^(5-3) = 2^2 = 4

Therefore, 2^5 divided by 2^3 equals 4.

It is important to note that the division property of exponents holds true for any non-zero base and any real exponents, as long as the base remains consistent throughout both the numerator and denominator of the division operation.

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