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WINSTONCH [101]
2 years ago
15

Write 6^4÷√6 as a single power of 6.

Mathematics
1 answer:
tamaranim1 [39]2 years ago
3 0

~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] ~\dotfill\\\\ 6^4\div \sqrt{6}\implies \cfrac{6^4}{\sqrt{6}}\implies \cfrac{6^4}{6^{\frac{1}{2}}}\implies 6^4\cdot 6^{-\frac{1}{2}} \\\\\\ 6^{4-\frac{1}{2}}\implies 6^{\frac{8-1}{2}}\implies 6^{\frac{7}{2}}

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the percent p of the u.s. population with internet access is given by 25p-34t=1378 where t is the number of years after 1990. wh
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the percent p of the u.s. population with internet access is given by:

25 p-34 t=1378

where t is the number of years after 1990.

  • We are asked to find  what percent of the u.s. population had internet access in 2005 i.e. we need to find the value of p after 15 years i.e. t=15.

⇒  25p-34×(15)=1378

⇒  25p-510=1378

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Hence, 75.52 percent of the u.s. population had internet access in 2005.

  • Next we are asked to find in what year will 89% have internet access?

i.e. we have to find the value of t when we are given p=89

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Hence after 25 years 89% will have internet access.

i.e. in the year 2015 89% will have internet access.



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