Which of the following is the equivalent expression to (2^-3x9^3)^-4/2^9x9^-10 that has been generated by applying the properties of integer exponents?A. 2^3x9^2 B. 2^12x9^-12/2^9x9^-10 C. 2^-7x9^-1/2^9x9^-10 D. 2^3/9^2
To simplify the expression using the properties of integer exponents, we can start by applying the power of a power property.
First, let's simplify (2^-3x9^3)^-4:
(2^-3x9^3)^-4 = 2^(-3*-4)x(9^3)^-4 = 2^12x9^-12
Next, let's simplify 2^9x9^-10:
2^9x9^-10 = 2^9/9^10
Now, let's substitute these simplified expressions back into the original expression:
(2^-3x9^3)^-4/2^9x9^-10 = (2^12x9^-12)/(2^9/9^10)
To divide two expressions with the same base, we can subtract the exponents:
= 2^(12-9)x9^(-12-10) = 2^3x9^-22
The equivalent expression that has been generated by applying the properties of integer exponents is:
A. 2^3x9^2