Questions: Multiply a^3 cdot a^-5

Multiply a^3 cdot a^-5
Transcript text: Multiply $a^{3} \cdot a^{-5}$
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Solution

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Solution Steps

Step 1: Understand the problem

We are asked to multiply \( a^{3} \cdot a^{-5} \). This involves using the laws of exponents.

Step 2: Apply the exponent rule

When multiplying terms with the same base, we add the exponents: \[ a^{m} \cdot a^{n} = a^{m+n}. \] Here, \( m = 3 \) and \( n = -5 \), so: \[ a^{3} \cdot a^{-5} = a^{3 + (-5)} = a^{-2}. \]

Step 3: Simplify the expression

A negative exponent means the reciprocal of the base raised to the positive exponent: \[ a^{-2} = \frac{1}{a^{2}}. \]

Final Answer

The correct answer is: \[ \boxed{\frac{1}{a^{2}}}. \]

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