Mathematics: 3^1/2 × a^2/3 × b^3/4 write as a single radical

36Step-by-step:I took the test and it was right...

3^1/2 × a^2/3 × b^3/4 write as a single radical

Ответ:

tristanortonubca

31.12.2021

Remember rules of exponents
$x^{ \frac{z}{y} } = \sqrt[y]{x^{z}}$
combine because another rule is
√x times √y=√(xy) so

if we can make the denomenator of all fractions the same, then we can have a common root so
2 3 and 4
common number is 12 so
convert bottom number to 12 so
1/2=6/12

2/3=8/12

3/4=9/12

so the equation is

$3^{ \frac{6}{12} }$ times $a^{ \frac{8}{12} }$ times $b^{ \frac{9}{12} }$
this equals

$\sqrt[12]{3^{6}}$ times $\sqrt[12]{a^{8}}$ times $\sqrt[12]{b^{9}}$

since we can combine we get
$\sqrt[12]{ 3^{6} a^{8} b^{9} }$

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Ответ:

darkskinnednune

23.01.2020

Mathematics

Step-by-step:

I took the test and it was right

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3^1/2 × a^2/3 × b^3/4
write as a single radical

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