Q:

# What Are Distributing Exponents?

A:

The distributive property of exponents is a mathematical rule that applies to an exponent that acts on a term that is within parentheses. It says that if there is a single term in the base, such as "3x," and it is raised to a certain power, like "(3x)^6," the exponent applies to all parts of the term, in this case to both the three and the "x."

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In the previous example, the distributive property of exponents says that "(3x)^6 = (3^6) (x^6)," and both forms can be used interchangeably.

In another example, "(8 x 4)^3" is the same as saying "(8^3) (4^3)." The problem can be simplified in two ways: (8 x 4)^3 = 32^3 = 32,768 and (8^3) (4^3) = (512) (64) = 32,768. Both ways are equally valid and will always yield the same results.

However, if there are any addition or subtraction terms within the parentheses, there is no longer a single term in the base, so the distributive property of exponents cannot be used in the same way. An example of this is: (6 + 3)^3 ≠ 6^3 + 3^3. This is clearly seen when the inequality is simplified: 9^3 ≠ 216 + 27, because 729 ≠ 243.