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Question Number 193213 by simplifiedmaths965 last updated on 07/Jun/23

$${\left(\frac{a^m}{a^{-n}}\right)}^{m-n}$$

Answered by aba last updated on 07/Jun/23

$${\left(\frac{{\mathrm{a}}^{\mathrm{m}}}{{\mathrm{a}}^{-\mathrm{n}}}\right)}^{\mathrm{m}-\mathrm{n}}={\left({\mathrm{a}}^{\mathrm{m}+\mathrm{n}}\right)}^{\mathrm{m}-\mathrm{n}}={\mathrm{a}}^{{\mathrm{m}}^2-{\mathrm{n}}^2}$$

Answered by Humble last updated on 07/Jun/23

$$a^{(m-(-n))m-n}$$$$a^{(m+n)(m-n)}$$$$a^{m(m-n)+n(m-n)}$$$$a^{m^2\cancel{-nm+nm}-n^2}$$$$a^{m^2-n^2}$$

Answered by MATHEMATICSAM last updated on 07/Jun/23

$${\left(\frac{a^m}{a^{-n}}\right)}^{m-n}$$$$={\left(a^{m+n}\right)}^{m-n}$$$$=a^{(m+n)(m-n)}$$$$=a^{m^2-n^2}$$$$$$

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