Use the power of power rule to rewrite each expression as a single exponent

1. ((-4)^-5)^-4
2.(8^3)^16
3. ((-2.3)^7/^2
4.((- 1/3)^-2/^-5
5.(5^12)^-3
6. ((5/4)^4)^13

just realize that since

u^n = u*u*u* ...*u (n times) then
(u^m)^n = u^m * u^m * ... * u^m (n times)
that is just u^(m+m+m...+m) (n times) = u^(mn)
so,
((-4)^-5)^-4 = (-4)^(-5 * -4) = (-4)^20 = 4^20

((- 1/3)^-2/^-5 ??? I assume you mean
((- 1/3)^-2)^-5
= (-1/3)^(-2 * -5) = (-1/3)^10 = (-3^-1)^10 = 3^-10 = 1/3^10

note that all even powers are positive, since negative * negative = positive

now you try the rest; post your work if you get stuck.
google can provide many more fine examples, discussions, and videos.

Rewrite the expression using exponet (2 to the power of 18) to the power of 8

Sure! To rewrite each expression as a single exponent using the power rule, we need to simplify the exponents step by step. Let's go through each expression one by one:

1. ((-4)^-5)^-4:
To apply the power rule, we multiply the exponents:
(-4)^((-5) * (-4)) = (-4)^20

2. (8^3)^16:
Similarly, we multiply the exponents:
8^(3 * 16) = 8^48

3. ((-2.3)^7)^2:
Since the expression has a nested exponent, we multiply the exponents:
(-2.3)^(7 * 2) = (-2.3)^14

4. ((-1/3)^(-2))^(-5):
Here, we have a negative exponent. To simplify, we invert the base and change the exponent sign:
((-1/3)^(2))^5 = ((3/-1)^(2))^5 = (3^2)^5 = 9^5

5. (5^12)^(-3):
Multiply the exponents:
5^(12 * -3) = 5^(-36)

6. ((5/4)^4)^13:
Multiply the exponents:
(5/4)^(4 * 13) = (5/4)^52

So, the expressions rewritten as single exponents are:

1. (-4)^20
2. 8^48
3. (-2.3)^14
4. 9^5
5. 5^(-36)
6. (5/4)^52