Question

Apply the Properties of Integer Exponents to generate equivalent expressions to ((7^(-0))*7^(20))/(6^(-2)) with only positive exponents, then solve the expression. Provide the answer as an improper fraction. (1 point)
((7^(-3))^(7)*7^(20))/(6^(-2))=

Answer 1

Starting with the given expression:

((7^(-0))*7^(20))/(6^(-2))

We can apply the property that any number raised to the power of 0 is equal to 1:

((1)*7^(20))/(6^(-2))

We can also apply the property that when there is a negative exponent in the numerator or denominator, it can be moved to the opposite position and the sign of the exponent changes:

(7^(20))/(6^(2))

Now we can solve the expression:

7^(20) = 7^(10+10) = (7^10)*(7^10)

6^(2) = 6 * 6

Therefore,

((7^(-0))*7^(20))/(6^(-2)) = ((1)*(7^10)*(7^10))/(6 * 6)

= (7^10)*(7^10)/(6 * 6)

In an improper fraction, this would be:

(7^10)*(7^10)/(6 * 6) = (7^10)/(6 * 6)

So the answer in improper fraction form is:

(7^10)/(6 * 6)