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 * 1 point 7/16 21/28 -7/16 16
To apply the properties of integer exponents, we can simplify the expression step by step:
Step 1: Rewrite the expression with only positive exponents.
(4^3 * 7^-2)^-5 becomes (4^3 * 1/7^2)^-5
Step 2: Simplify the exponents inside the parentheses.
(4^3 * 1/7^2)^-5 = (64 * 1/49)^-5
Step 3: Multiply the numbers inside the parentheses.
(64 * 1/49)^-5 = (64/49)^-5
Step 4: Apply the negative exponent rule, which states that (a/b)^-c = (b/a)^c.
(64/49)^-5 = (49/64)^5
Step 5: Evaluate the expression.
(49/64)^5 = 49^5 / 64^5
Step 6: Simplify the numerator and denominator.
49^5 = 5764801
64^5 = 1073741824
Therefore, the final answer is 5764801/1073741824, which cannot be simplified further.