Apply the Properties of Integer Exponents to generate equivalent expressions with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.
(4^3 * 7^-2)^-5 / 7^9 * 4^-13
is the answer
7/16
or
21/28
or
-7/16
or
16
To apply the properties of integer exponents, we can rewrite the given expression as follows:
(4^3 * 7^-2)^-5 / 7^9 * 4^-13
= (4^3)^-5 * (7^-2)^-5 / 7^9 * 4^-13
= 4^-15 * 7^10 / 7^9 * 4^-13
Now, let's simplify each term separately:
4^-15 = 1/4^15 = 1/(4^3)^5 = 1/64^5
7^10 / 7^9 = (7^10) / (7^9) = 7^(10-9) = 7^1 = 7
So, our expression becomes:
1/64^5 * 7 / 4^-13
Now, let's simplify the second term:
4^-13 = 1/4^13 = 1/(4^3)^4 = 1/64^4
Substituting those values back into the expression:
1/64^5 * 7 / 1/64^4
= (1/64^5) * (7/1) * (64^4/1)
= (1 * 7 * 64^4) / (64^5)
= 7 * 64^4 / 64^5
= 7 * (64^4 / 64^5)
= 7 * (1/64) (64^4 / 64^5 simplifies to 1/64 because any number raised to the power 0 is always 1)
= 7/64
So, the simplified fraction with no remaining exponents is 7/64.