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Work out: 3^(4n) * 3^(-2n) / 3ⁿ = 32

July 28, 2026Mathematics

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Answer

n = \mathbf{2}

3 steps

Ili kutatua tatizo hili, tutatumia sheria za vipeo (exponents).

Rahisisha namba (numerator) ya usemi kwa kutumia sheria ya vipeo $a^m \times a^n = a^{m+n}$ .
$3^{4n} \times 3^{-2n} = 3^{4n + (-2n)} = 3^{4n - 2n} = 3^{2n}$
Sasa usemi umekuwa $\frac{3^{2n}}{3^n}$ .
Rahisisha usemi huu kwa kutumia sheria ya vipeo $\frac{a^m}{a^n} = a^{m-n}$ .
$\frac{3^{2n}}{3^n} = 3^{2n - n} = 3^n$
Linganisha matokeo na upande wa kulia wa mlinganyo, ambao ni $3^2$ .
$3^n = 3^2$
Kwa kuwa besi (base) ni sawa (3), vipeo (exponents) lazima viwe sawa.
$n = 2$

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