Question
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wing sad leave your answer in exponeutial fo (2) \( \frac{23^{9} \times 11^{3}}{23^{17} \times 11^{4}} \)

Ask by King Beck. in South Africa
Feb 20,2025

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Tutor-Verified Answer

Answer

The expression simplifies to \( \frac{1}{11 \times 23^{8}} \) or approximately \( 1.160873 \times 10^{-12} \).

Solution

Calculate or simplify the expression \( (23^9 * 11^3) / (23^17 * 11^4) \). Calculate the value by following steps: - step0: Calculate: \(\frac{\left(23^{9}\times 11^{3}\right)}{\left(23^{17}\times 11^{4}\right)}\) - step1: Remove the parentheses: \(\frac{23^{9}\times 11^{3}}{23^{17}\times 11^{4}}\) - step2: Multiply by \(a^{-n}:\) \(23^{9}\times 11^{3}\times 23^{-17}\times 11^{-4}\) - step3: Multiply the terms: \(23^{9-17}\times 11^{3}\times 11^{-4}\) - step4: Subtract the numbers: \(23^{-8}\times 11^{3}\times 11^{-4}\) - step5: Multiply the terms: \(23^{-8}\times 11^{3-4}\) - step6: Subtract the numbers: \(23^{-8}\times 11^{-1}\) - step7: Rewrite the expression: \(\frac{1}{23^{8}}\times \frac{1}{11}\) - step8: Multiply the fractions: \(\frac{1}{23^{8}\times 11}\) - step9: Multiply: \(\frac{1}{11\times 23^{8}}\) The expression \( \frac{23^{9} \times 11^{3}}{23^{17} \times 11^{4}} \) simplifies to \( \frac{1}{11 \times 23^{8}} \) or approximately \( 1.160873 \times 10^{-12} \) in exponential form.

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The Deep Dive

To simplify the expression \( \frac{23^{9} \times 11^{3}}{23^{17} \times 11^{4}} \), you can use the property of exponents that states \( \frac{a^m}{a^n} = a^{m-n} \). Starting with the \(23\) terms, we have: \[ \frac{23^{9}}{23^{17}} = 23^{9-17} = 23^{-8} \] Now for the \(11\) terms: \[ \frac{11^{3}}{11^{4}} = 11^{3-4} = 11^{-1} \] Putting it all together, we get: \[ \frac{23^{9} \times 11^{3}}{23^{17} \times 11^{4}} = 23^{-8} \times 11^{-1} \] This can be expressed in exponential form as: \[ \frac{1}{23^{8} \times 11} \] So the final answer in exponential form is: \[ 23^{-8} \times 11^{-1} \]

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