Question

Given the following expressions:

5 with an exponent of 3 times 5 with an exponent of -4
exponent of 3 times (1/4) with an exponent of 2
(1/4) with an exponent of 3 times (1/4) with an exponent of 2
(-7) with an exponent of 5 over (-7) with an exponent of 7
Part 1: Use operations of exponents to simplify each expression (A-D). Include your work in your final answer.

Part 2: For each simplified expression (A-D), tell whether or not the expression has a value between 0 and 1.

Answer 1

Explanation:

Step 1:

A . 5 with an exponent of 3 times 5 with an exponent of -4

= = = = 1/5

B . (1/4) with an exponent of 3 times (1/4) with an exponent of 2

=

C. Same as above

D.

Step 2 :

All the above expressions have a value between 1 and 2

Answer 2

Explanation:

Step 1:

A . 5 with an exponent of 3 times 5 with an exponent of -4

=
`5^(3) * 5^(-4)` =
`5^(3-4)`=
`5^(-1)` = 1/5

B . (1/4) with an exponent of 3 times (1/4) with an exponent of 2

=
`(1/4)^(3) * (1/4)^(2) = (1/4)^(3+2) = (1/4)^(5) = 1/1024`

C. Same as above

D.
`\\((-7)^(5) )/((-7)^(7) ) = (-7)^(5-7) = (-7)^(-2) =1/7^(2) = 1/49`

Step 2 :

All the above expressions have a value between 1 and 2