How do you multiply 9th root of 9x squared times 6th root of 27 x raise to 5?

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How do you multiply 9th root of 9x squared times 6th root of 27 x raise to 5?

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Answer 1 · 2018-06-28T10:56:14

The 27th root of 729x raised to the 5th power.

Explanation:

9th root of 9x squared can be written as
$XXX {(9 x)}^{\frac{2}{9}} = {(3^{2})}^{\frac{2}{9}} \cdot x^{\frac{2}{9}}$ $color(white)("XXX")(9x)^(2/9)=(3^2)^(2/9) * x^(2/9)$
$XXXXXX = 3^{\frac{4}{9}} \cdot x^{\frac{2}{9}}$ $color(white)("XXXXXX")=3^(4/9) * x^(2/9)$

6th root of 27x raised to 5 can be written as
$XXX {(27 x)}^{\frac{5}{6}} = {(3^{3})}^{\frac{5}{6}} \cdot x^{\frac{5}{6}}$ $color(white)("XXX")(27x)^(5/6)=(3^3)^(5/6) * x^(5/6)$
$XXXXXXX = 3^{\frac{15}{6}} \cdot x^{\frac{5}{6}}$ $color(white)("XXXXXXX")=3^(15/6) * x^(5/6)$
$XXXXXXX = 3^{\frac{5}{2}} \cdot x^{\frac{5}{6}}$ $color(white)("XXXXXXX")=3^(5/2) * x^(5/6)$

${(9 x)}^{\frac{2}{9}} \times {(27 x)}^{\frac{5}{6}}$ $(9x)^(2/9) xx (27x)^(5/6)$

$XXX = 3^{\frac{4}{9}} \cdot x^{\frac{2}{9}} \times 3^{\frac{5}{2}} \cdot x^{\frac{5}{6}}$ $color(white)("XXX")=3^(4/9) * x^(2/9) xx 3^(5/2) * x^(5/6)$

$XXX = 3^{\frac{4}{9}} \cdot 3^{\frac{5}{2}} \times x^{\frac{2}{9}} \cdot x^{\frac{5}{6}}$ $color(white)("XXX")=3^(4/9) * 3^(5/2) xx x^(2/9) * x^(5/6)$

$XXX = 3^{\frac{10}{9}} \cdot x^{\frac{5}{27}}$ $color(white)("XXX")=3^(10/9) * x^(5/27)$

$XXX = 3^{\frac{30}{27}} \cdot x^{\frac{5}{27}}$ $color(white)("XXX")=3^(30/27) * x^(5/27)$

$XXX = {(3^{6})}^{\frac{5}{27}} \cdot x^{\frac{5}{27}}$ $color(white)("XXX")=(3^6)^(5/27) * x ^(5/27)$

$XXX = 729^{\frac{5}{27}} \cdot x^{\frac{5}{27}}$ $color(white)("XXX")=729^ (5/27) * x^(5/27)$

$XXX = {(729 x)}^{\frac{5}{27}}$ $color(white)("XXX")=(729x)^(5/27)$

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How do you multiply 9th root of 9x squared times 6th root of 27 x raise to 5?

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