apply the properties of integer exponent to generate equivalent expressions to (7^-3)*7^20

Question

with only positive exponents then solve the expression provide the answer as an improper fraction

Answer 1

To generate equivalent expressions with positive exponents, we can use the property of integer exponents which states that a^(-n) = 1/a^n.

First, let's rewrite the expression using this property:

(7^-3)*7^20 = 1/(7^3)*7^20

Next, we can use the property of multiplying exponential expressions with the same base, which states that a^n * a^m = a^(n+m):

= 1/(7^(3+20))

Now, we can simplify the exponent:

= 1/(7^23)

To solve the expression, we can calculate 7^23 and express the answer as an improper fraction:

7^23 = 3,200,182,748,371

Therefore, the simplified expression is:

1/3,200,182,748,371 = 1/3200182748371

So the answer is 1/3200182748371, which is an improper fraction.