4^3x7^-2)^-5/ 7^9

Answer 1

To simplify the expression 4^3 * 7^-2)^-5 / 7^9, we can start by simplifying the inside parentheses first.

Inside the parentheses, we have 4^3 * 7^-2.
First, evaluate 4^3:
4^3 = 4 * 4 * 4 = 64.

Next, evaluate 7^-2:
7^-2 = 1 / 7^2 = 1 / 49.

Now, the expression inside the parentheses simplifies to 64 * (1/49).

Let's write the expression again: (64 * 1/49)^-5 / 7^9.

Now, simplify (64 * 1/49)^-5:
(64 * 1/49)^-5 = (64 / 49)^-5.

Since the base is the same, we can simplify by multiplying the exponents:
(64 / 49)^-5 = 64^-5 / 49^-5.

Evaluate 64^-5:
64^-5 = 1 / 64^5 = 1 / (64 * 64 * 64 * 64 * 64) = 1 / 1073741824.

Evaluate 49^-5:
49^-5 = 1 / 49^5 = 1 / (49 * 49 * 49 * 49 * 49) = 1 / 5764801.

Now, the expression simplifies to (1 / 1073741824) / (1 / 5764801).

To divide by a fraction, we can multiply by the reciprocal of the fraction:
(1 / 1073741824) / (1 / 5764801) = (1 / 1073741824) * (5764801 / 1).

Multiplying the fractions gives us:
(1 * 5764801) / (1073741824 * 1) = 5764801 / 1073741824.

Finally, simplify 7^9:
7^9 = 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 = 40353607.

Therefore, the simplified expression is 5764801 / 1073741824 / 40353607.