Question

Apply the Property of Negative Integer Exponents to generate an expression equivalent to 7^−3⋅7^−5 with positive exponents only.
Fill in the blank

Answer 1

Recall that according to the property of negative exponents, for any nonzero number a, a^(-n) is equal to 1/a^n.
Therefore, we can rewrite the expression 7^(-3) ⋅ 7^(-5) as 1/7^3 ⋅ 1/7^5.

Now, in order to transform this expression into one with positive exponents only, we can simplify the expression further.

1/7^3 ⋅ 1/7^5 = 1/(7^3 ⋅ 7^5)

Using the property of exponents, when we multiply two numbers with the same base, we add the exponents. Therefore,

1/(7^3 ⋅ 7^5) = 1/7^(3 + 5)

Simplifying the exponent, we have:

1/7^8

Therefore, an expression equivalent to 7^(-3) ⋅ 7^(-5) with positive exponents only is 1/7^8.