Video: Simplifying Expressions Using Laws of Exponents

Which of the following is equal to 7⁵ + 7⁵ + 7⁵ + 7⁵ + 7⁵ + 7⁵? [A] 49⁵ [B] 7³⁵ [C] 7⁴² [D] 7⁶.

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Video Transcript

Which of the following is equal to seven to the fifth power plus seven to the fifth power plus seven to the fifth power plus seven to the fifth power plus seven to the fifth power plus seven to the fifth power? a) 49 to the fifth power, b) seven to the 35th power, c) seven to the 42nd power, or d) seven to the sixth power.

This expression is a problem of repeated addition, and we want to simplify this somehow. We can simplify this expression by taking the repeated addition and turning it into multiplication. Seven to the fifth power is being added to itself seven times. We have seven to the fifth power seven times.

We can simplify that by saying seven to the fifth power times seven. The whole number seven is the same thing as seven to the first power. And when we’re multiplying two powers with the same base — here we have a base seven, seven to the fifth power and seven to the first power — what we need to do is keep the base the same and add the exponents together.

We simplify that by saying seven to the five plus one power, seven to the sixth power. Adding seven to the fifth power together seven times is the same thing as taking seven to the sixth power.

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