Answer:
(A) 5^3 * 5^-4
= 5^(3-4)
= 5^(-1)
= 5^-1
= 1/5^1
= 0.2
Yes, expression has value between 0 and 1
(B) 3^5 / 3^-6
= 3^5 * 3^6
= 3^(5+6)
= 3^(11)
= 177147
No, expression does not have value between 0 and 1
(C) (1/4)^3 * (1/4)^2
= (1/4)^(3+2)
= (1/4)^(5)
= (1^5/4^5)
= 1 / 4^5
= 1 / 1024
= .000977
Yes, expression has value between 0 and 1
(D) (-7)^5 / (-7)^7
= (-7)^5 * (-7)^-7
= (-7)^(5-7)
= (-7)^(-2)
= 1 / (-7)^2
= 1 / 49
= 0.02041
Yes, expression has value between 0 and 1
Explanation:
For these problems we need to know a few things:
(1) Powers of like bases, you add the exponent
This means the following:
x^y * x^z = x^(y+z)
Or
x^y / x^z = x^(y-z)
(2) Negative powers can be swapped on the fraction to be positive
This means the following:
x^-y = 1 / x^y
Or
1 / x^-y = x^y
Using these two things, we can easily simplify all the expressions given.
Cheers.