Question

1.Simplify 5 to the 5th over 5 to the 8th.

1 over 5 to the 3rd power

5 to the 3rd power

1 over 25

1 over 5 to the negative 3rd


2.In which expression should the exponents be multiplied?

(53)−4

one third to the 4th times one third to the 7th

3 to the 7th over 3 to the 15th

45 ⋅ 42

Answer 1

it is (A) 1 over 5 to the 3rd power

Explanation:

Answer 2

Q1. The answer is 1 over 5 to the 3rd power.

5 to the 5th is 5⁵
5 to the 8th is 5⁸
5 to the 5th over 5 to the 8th is
`( 5^(5) )/( 5^(8) )`
To simplify, we will use two rules:

`( x^(a))/( x^(b) ) = x^(a-b) \\ x^(-a) = (1)/( x^(a))`
Therefore:

`( 5^(5) )/( 5^(8) ) = 5^(5-8) =5^(-3)= (1)/(5^(3))`

`(1)/(5^(3))` is the same as 1 over 5 to the 3rd power.


Q2. The answer is (53)−4.

The exponents are multiplied when are expressed in the form:

`(x^(a)) ^(b)= x^(a*b)`
So,
`(5^(3) )^(-4)=5^(3*(-4))=5^(-12)`

Other choices are incorrect:
one third to the 4th times one third to the 7th is
`image`
3 to the 7th over 3 to the 15th is
`( 3^(7) )/(3^(15)) =3^(7-15)`
45 ⋅ 42 is
`4^(5)* 4^(2) = 4^(5+2)`