(4^3*7^-2)*-5/7^9*4^-13

Question

Without an exponent

Answer 1

To solve this expression, let's break it down step by step:

Step 1: Simplify the exponents:
4^3 = 4 * 4 * 4 = 64
7^-2 = 1 / (7^2) = 1 / (7 * 7) = 1 / 49
4^-13 = 1 / (4^13)

Step 2: Multiply the numbers with the same base:
(64 * -5) / 49 * (1 / (4^13))

Step 3: Simplify further:
-320 / 49 * (1 / (4^13))

Step 4: Simplify the exponent:
4^13 = 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 = 67,108,864

Step 5: Substitute the simplified exponent back into the expression:
-320 / 49 * (1 / 67,108,864)

Step 6: Multiply and divide:
(-320) / (49 * 67,108,864)

Step 7: Simplify further:
-320 / 3,290,366,272

So the final answer is -320 / 3,290,366,272.