(4^3*7^-2)^-5/7^9*4^-13= Your answer will be a simplified fraction with no remaining exponents.
To simplify the expression, let's evaluate the exponents separately:
The exponent of the numerator: (-5)
(4^3 * 7^-2)^(-5) = (4^(3*(-5))) * (7^(-2*(-5)))
= 4^(-15) * 7^10
= 7^10 / 4^15
The exponent of the denominator: (7^9 * 4^(-13))
So, the simplified fraction is:
(7^10 / 4^15) / (7^9 * 4^(-13))
We can rewrite this as:
(7^10 / 7^9) * (4^(-13) / 4^15)
= 7^(10-9) * 4^(-13-15)
= 7^1 * 4^(-28)
Finally, the simplified fraction is:
7 * 1/4^28
= 7/4^28
Therefore, the answer is 7/4^28.