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(5) \( \frac{1}{3 x^{-5}} \)

Ask by Macdonald Ruiz. in South Africa
Mar 09,2025

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Answer

The simplified form is \( \frac{x^5}{3} \).

Solution

Calculate or simplify the expression \( 1/(3*x^(-5)) \). Simplify the expression by following steps: - step0: Solution: \(\frac{1}{\left(3x^{-5}\right)}\) - step1: Remove the parentheses: \(\frac{1}{3x^{-5}}\) - step2: Rewrite the expression: \(\frac{1}{\frac{3}{x^{5}}}\) - step3: Simplify: \(\frac{x^{5}}{3}\) The simplified form of \( \frac{1}{3x^{-5}} \) is \( \frac{x^5}{3} \).

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Let's simplify the expression \( \frac{1}{3 x^{-5}} \). You can start by recalling that \( x^{-n} \) is the same as \( \frac{1}{x^n} \). Therefore, \[ x^{-5} = \frac{1}{x^5}. \] Substituting this into the original expression, we have: \[ \frac{1}{3 \cdot \frac{1}{x^5}} = \frac{x^5}{3}. \] So, the simplified form becomes \( \frac{x^5}{3} \). Now, isn't that simpler? Just remember, negative exponents flip the base! For a bit of fun, think of exponents like a magic spell. When you see that minus sign, imagine it flipping your spell out of existence and bringing in its reciprocal – poof! You just simplified your problem with a wave of your wand!

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