C. ![\frac{1}{45^{6}}](/tpl/images/0857/7067/078cf.png)
Step-by-step explanation:
Concepts Used:
ExponentsThe rule of Negative exponentsPower of a Product Rule
Simplifying the given expression:
We are given the expression:
![\frac{45^{-3}}{45^{3}}](/tpl/images/0857/7067/82533.png)
According to the rule of negative exponents, 45⁻³ = 1/45³
![\frac{1}{45^{3}}*\frac{1}{45^{3}}](/tpl/images/0857/7067/a037f.png)
![\frac{1}{45^{3}*45^{3}}](/tpl/images/0857/7067/af747.png)
According to the Power of a Product rule: aⁿ X aᵇ = aⁿ⁺ᵇ
Using the Power rule to further simplify our expression:
![\frac{1}{45^{6}}](/tpl/images/0857/7067/078cf.png)
Hence, Option C is correct