Question

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

7/16
or
21/28
or
-7/16
or
16

Answer 1

[AI-generated answer — Bot GPT 3.5]

To apply the properties of integer exponents, we can start by using the rule that states "a^(-n) = 1/(a^n)".

1. (4^3 * 7^-2)^-5 / 7^9 * 4^-13
2. (64 * 1/(49))^(-5) / 7^9 * 1/(2^26)
3. (64/49)^(-5) / 7^9 * 1/(2^26)
4. (49/64)^5 / 7^9 * 1/(2^26)
5. (7/8)^5 / 7^9 * 1/(2^26)
6. 16807/32768 / 7^9 * 1/(2^26)
7. 16807/32768 / (7^9 * 2^26)

We can simplify the expression further by applying the rule that states "a^m / a^n = a^(m-n)".

8. 16807/(32768 * 7^9 * 2^26)

To simplify the expression, we can rewrite the denominator as a power of 2.

32768 = 2^15

9. 16807/(2^15 * 7^9 * 2^26)

By applying the property "a^m * a^n = a^(m+n)", we can simplify the expression further.

2^15 * 2^26 = 2^(15+26) = 2^41

10. 16807/(2^41 * 7^9)

Since there are no more exponents in the expression, we have simplified the expression.

Therefore, the expression is 16807/(2^41 * 7^9).