Find the value of $95^{-17} \div 95^{9} \times 95^{-15}$.

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This question was previously asked in

RRB NTPC 2024 CBT 1 Question Paper (28-Aug-2025) (Shift 3)

$95^{-49}$

$95^{-41}$

$95^{-35}$

$95^{-42}$

The correct answer is

$95^{-41}$

The expression to solve is $95^{-17} \div 95^{9} \times 95^{-15}$.
To simplify the expression, we use the laws of exponents. One of the key properties states: $a^m \div a^n = a^{m-n}$ and $a^m \times a^n = a^{m+n}$.
Applying the division rule to the first two terms gives: $95^{-17} \div 95^{9} = 95^{-17 - 9} = 95^{-26}$.
Now, we multiply the result by the third term using the multiplication rule: $95^{-26} \times 95^{-15} = 95^{-26 + (-15)} = 95^{-41}$.
Therefore, the value of the expression is $95^{-41}$.

The correct answer is $95^{-41}$, which corresponds to option: $95^{-41}$.

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