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Exponents with like Bases

If m and n ar...

Question

If $m$ and $n$ are integers, $a$ is a non-zero integer and $a^{m}$ × $a^{n}$ = $a^{x}$ , then the value of $x$ is _____.

m n

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m - n

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m + n

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\frac{m}{n}

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Solution

The correct option is C $m + n$
We have $a^{m} \times a^{n} = a^{m + n},$ where $a$ , $m$ and $n$ are integers, $a \neq 0.$
Given $a^{m} \times a^{n} = a^{x}$
$⟹ a^{m + n} = a^{x}$
$⟹ x = m + n$

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$x^{m} \times x^{n} = x^{m + n},$ where $x$ is a non-zero rational number and $m, n$ are positive integers.

If $m$ and $n$ are integers, $a$ is a non-zero integer and $a^{m}$ × $a^{n}$ = $a^{x}$ , then the value of $x$ is _____.

a

m and n

a^{m} \times a^{n} =

a

b

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a^{- m} \times a^{m}

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