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).
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
1 answer