Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

How do you simplify ${(5^{\sqrt{2}})}^{\sqrt{8}}$ $(5^sqrt2)^sqrt8$ ?

1 Answer

Oct 29, 2016

${(5^{\sqrt{2}})}^{\sqrt{8}} = 625$ $(5^sqrt(2))^sqrt(8) = color(green)(625)$

Explanation:

For the general case
$XXX {(x^{a})}^{b} = x^{a b}$ $color(white)("XXX")(x^a)^b= x^(ab)$

So
$XXX {(5^{\sqrt{2}})}^{\sqrt{8}} = 5^{\sqrt{16}} = 5^{4} = 625$ $color(white)("XXX")(5^sqrt(2))^sqrt(8) = 5^sqrt(16)=5^4=625$

Related questions

See all questions in Exponential Growth and Decay

Impact of this question

1595 views around the world

You can reuse this answer
Creative Commons License