Question

If (–3)^m+1 × (–3)^5 = (–3)^7, then the value of m is:
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Answer 1

$\large{\underline{\underline{\bigstar\bigstar \: Method \: 1 : }}}$

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$\bf{\underline{\underline{\bigstar\bigstar \: Formula \: used : }}}$

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• $\footnotesize{ a^x \times a^y = a^{x + y }}$

• $\footnotesize{ a^x = a^y \implies x = y }$

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$\bf{\underline{\underline{\bigstar\bigstar \: Solution : }}}$

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$\footnotesize{ (–3)^{m+1} \times (–3)^5 = (–3)^7 }$

$\footnotesize{\implies (–3)^{m + 1 + 5} = (–3)^7}$

$\footnotesize{\implies (–3)^{m + 6} = (–3)^{7}}$

$\footnotesize{\implies m + 6 = 7}$

$\footnotesize{\implies m = 7 - 6}$

$\footnotesize{\implies m = 1}$

$\footnotesize{\implies m = 1}$

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$\bold{\underline{\therefore \: Value \: of \: m \: is \: 1 }}$