NIMCET 2022 — Mathematics PYQ

To solve this expression, we use the basic laws of exponents and the fundamental property of logarithms.

1. Apply Laws of Exponents

The given expression is $3^{3-{\log }_{3}5}$.

Using the quotient rule for exponents, $a^{m-n}=\frac{a^m}{a^n}$, we can rewrite the expression as:

$$3^{3-{\log }_{3}5}=\frac{3^3}{3^{{\log }_{3}5}}$$

2. Apply Logarithmic Property

We use the fundamental identity for logarithms:

$$a^{{\log }_{a}x}=x$$

Applying this to the denominator $3^{{\log }_{3}5}$, we get:

$$3^{{\log }_{3}5}=5$$

3. Final Calculation

Now, substitute the values back into our fraction:

$$\frac{3^3}{3^{{\log }_{3}5}}=\frac{27}{5}$$

Correct Option: B) $\frac{27}{5}$