Problem

Rewrite the expression using a positive exponent. \[ 3.5^{-9} \cdot 3.5^{5} \] \[ 3.5^{-9} \cdot 3.5^{5}= \] (Simplify your answer. Type exponential notation with a positive exponent.)

Solution

Step 1 :Rewrite the expression using a positive exponent: \(3.5^{-9} \cdot 3.5^{5}\)

Step 2 :According to the rule of exponents, when you multiply two exponents with the same base, you add the powers. So, we can add -9 and 5 to get the new exponent: \(-9 + 5 = -4\)

Step 3 :The new exponent is -4. However, the expression needs to be rewritten with a positive exponent. To do this, we can use the rule that \(a^{-n} = \frac{1}{a^n}\). So, we can rewrite \(3.5^{-4}\) as \(\frac{1}{3.5^{4}}\)

Step 4 :Simplify the expression to get the final answer: \(\boxed{0.006663890045814244}\)

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Source: https://solvelyapp.com/problems/46038/

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