Which of the following is the equivalent expression to (5^-13x4^7)^0/4^-3 that has been generated by applying the properties of integer exponents? A. 1/64 B. 60/4^-3 C. 64 D. 1x4^-3
To simplify the expression (5^-13 * 4^7)^(0/4^-3), we can first simplify the exponents in the parenthesis.
Remember that
(a^m)^n = a^(m*n)
(5^-13 * 4^7)^(0/4^-3) = (5^(-13*0) * 4^(7*0))/(4^-3)
Since any number raised to the power of zero is equal to 1, we have:
(5^0 * 4^0)/(4^-3) = (1 * 1)/(4^-3)
Using the property that a^(-n) = 1/a^n, we can rewrite the denominator:
(1 * 1)/(1/(4^3)) = 1 * 4^3 = 4^3
Therefore, the equivalent expression is 4^3, which is option C.