Which expressions are equivalent to 7^-2•7^6 Choose two answers

A.7^2/7^-2

B.7^6/7^-2

C.7^-12

D.(7^2)^2

Explanation:

The expression 7^(-2)*7^6 simplifies to 7^4

We use the rule a^b*a^c = a^(b+c). In this case a = 7, b = -2, c = 6

In short, we add the exponents.

In choice A, we use the rule (a^b)/(a^c) = a^(b-c) where we're now subtracting the exponents.

Here we have the exponents subtract to b-c = 2-(-2) = 2+2 = 4. This shows that (7^2)/(7^(-2)) = 7^4

This is why choice A is one equivalent expression.

Choice D is the other equivalent expression since

(7^2)^2 = 7^(2*2) = 7^4

The rule used here is (a^b)^c = a^(b*c). We're multiplying exponents now.

Alternatively you can find that 7^(-2)*7^6 = 2401 through use of a calculator.

Then go through each answer choice to see which also produce a result of 2401.

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