Question
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
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
Answers
oobleck
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.
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.
Jamyah
Rewrite the expression using exponet (2 to the power of 18) to the power of 8