Question

1) Which expression is equivalent to 45^-3/45^3

A 45^-1
B 45^0
C 1/45^6
D 45^6

Answer 1

C.
`(1)/(45^(6))`

Explanation:

Concepts Used:

• Exponents
• The rule of Negative exponents
• Power of a Product Rule

Simplifying the given expression:

We are given the expression:

`(45^(-3))/(45^(3))`

According to the rule of negative exponents, 45⁻³ = 1/45³

`(1)/(45^(3))*(1)/(45^(3))`

`(1)/(45^(3)*45^(3))`

According to the Power of a Product rule: aⁿ X aᵇ = aⁿ⁺ᵇ

Using the Power rule to further simplify our expression:

`(1)/(45^(6))`

Hence, Option C is correct