Question

Determine the value of y^12 when y= 10^ -1/6​

Answer 1

`~\hspace{7em}\textit{negative exponents} \\\\ a^(-n) \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^(-n)} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^(-m)\implies a^(n-m) \\\\[-0.35em] ~\dotfill\\\\ y^(12)\hspace{5em}y=10^{-(1)/(6)}\qquad \implies \qquad \left( 10^{-(1)/(6)}\right)^(12)\implies 10^{-(1)/(6)\cdot 12} \\\\\\ 10^(-2)\implies \cfrac{1}{10^2}\implies \cfrac{1}{100}`

Answer 2

Answer:
`\boxed{(1)/(100)\ or\ 0.01}`

Explanation:

Determine the value of
`y^(12) \ when\ y=10^{-(1)/(6)`

`=(10^{-(1)/(6) })^(12)`

`=(1)/(100)\ or\ 0.01`