If (-3)^-5 =1/x, what is the value of x?

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25-08-2017
Mathematics

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If (-3)^-5 =1/x, what is the value of x?

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jdoe0001 jdoe0001 · Answer 1 · 2017-08-25T22:22:34+02:00

[tex]\bf \left.\qquad \qquad \right.\textit{negative exponents}\\\\ a^{-{ n}} \implies \cfrac{1}{a^{ n}} \qquad \qquad \cfrac{1}{a^{ n}}\implies a^{-{ n}} \qquad \qquad a^{{{ n}}}\implies \cfrac{1}{a^{-{{ n}}}}\\\\ -------------------------------\\\\ %(-3)^-5 =1/x, (-3)^{-5}=\cfrac{1}{x}\implies \cfrac{1}{(-3)^5}=\cfrac{1}{x}\implies 1\cdot x=(-3)^5\cdot 1\implies x=(-3)^5 \\\\\\ x=(-3)(-3)(-3)(-3)(-3)\implies x=-243[/tex]