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Simplify \( 24\left[\frac{3}{4}\right]^{n-1} \)

Ask by Franklin Bryant. in Nigeria
Jan 21,2025

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Tutor-Verified Answer

Answer

The simplified form is \( \frac{24 \times 3^{n-1}}{4^{n-1}} \).

Solution

Calculate or simplify the expression \( 24*(3/4)^(n-1) \). Simplify the expression by following steps: - step0: Solution: \(24\left(\frac{3}{4}\right)^{n-1}\) - step1: Expand the expression: \(24\times \frac{3^{n-1}}{4^{n-1}}\) - step2: Multiply the terms: \(\frac{24\times 3^{n-1}}{4^{n-1}}\) The simplified form of \(24\left[\frac{3}{4}\right]^{n-1}\) is \(\frac{24 \times 3^{n-1}}{4^{n-1}}\).

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Bonus Knowledge

To simplify \( 24\left[\frac{3}{4}\right]^{n-1} \), we start with the expression as is. This means we take the term \( \left[\frac{3}{4}\right]^{n-1} \) which indicates \( \frac{3}{4} \) raised to the power of \( n-1 \). Considering the coefficients and powers, the simplified expression remains: \[ 24 \cdot \left(\frac{3}{4}\right)^{n-1} \] This shows that for any integer \( n \), you multiply 24 by the fraction raised to the power \( n-1 \). There isn't further simplification without knowing specific values for \( n \), but that's about as simplified as the expression can get in general terms.

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