Questions: Simplify 9^-3/9^5. A 1/9^2 B 1/9^8 C 9^2 D 9^8

Simplify 9^-3/9^5. A 1/9^2 B 1/9^8 C 9^2 D 9^8
Transcript text: Simplify $\frac{9^{-3}}{9^{5}}$. A $\frac{1}{9^{2}}$ B $\frac{1}{9^{8}}$ C $\quad 9^{2}$ D $9^{8}$
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Solution

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Solution Steps

Step 1: Apply the Quotient Rule for Exponents

The expression \(\frac{9^{-3}}{9^{5}}\) can be simplified using the quotient rule for exponents, which states that \(\frac{a^m}{a^n} = a^{m-n}\). Applying this rule:

\[ \frac{9^{-3}}{9^{5}} = 9^{-3 - 5} = 9^{-8} \]

Step 2: Rewrite the Negative Exponent

A negative exponent can be rewritten as the reciprocal of the base raised to the positive exponent. Therefore:

\[ 9^{-8} = \frac{1}{9^{8}} \]

Step 3: Match with the Given Options

The simplified form \(\frac{1}{9^{8}}\) matches option B.

Final Answer

\[ \boxed{\text{B}} \]

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