Question

# ${a}^{m}×{a}^{n}$ is equal to

A

${a}^{m+n}$

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B

${a}^{m-n}$

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C

${a}^{mn}$

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D

${a}^{n-m}$

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Solution

## The correct option is A ${a}^{m+n}$Since the base $a$ is same and power $m$ and $n$ are different.When we multiply two numbers with same base but different powers, then according to law of exponents the base remains same and power adds.Therefore,${a}^{m}×{a}^{n}={\left(a\right)}^{m+n}$So, ${\mathbit{a}}^{\mathbf{m}}\mathbf{×}{\mathbit{a}}^{\mathbf{n}}\mathbf{}\mathbf{=}\mathbf{}{\mathbf{a}}^{\mathbf{m}\mathbf{+}\mathbf{n}}$.Hence, the correct option is (a).

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