Question

Simplify fourth root of 6 over fifth root of 6. 6 to the power of one fifth 6 to the power of nine twentieths 6 to the power of one twentieth 6 to the power of five fourths

Answer 1

6 1/20

Step-by-step explanation:

Answer 2

`\sqrt[20]{6}`

`\sqrt[60]{6^(137) }`

Explanation:

We have to simplify the followings:

1)
`\frac{\sqrt[4]{6} }{\sqrt[5]{6} }` and

2)
`6^{(1)/(5)} * 6^{(9)/(12)} * 6^{(1)/(12)} * 6^{(5)/(4)}`

1) Now,
`\frac{\sqrt[4]{6} }{\sqrt[5]{6} }`

=
`\frac{6^{(1)/(4)}}{6^{(1)/(5)}}`

=
`6^{((1)/(4) - (1)/(5))}`

{Since,
`(a^(b))/(a^(c)) = a^((b - c))` }

=
`6^{((5 - 4)/(20))}`

=
`6^{(1)/(20)}`

=
`\sqrt[20]{6}` (Answer)

2)
`6^{(1)/(5)} * 6^{(9)/(12)} * 6^{(1)/(12)} * 6^{(5)/(4)}`

=
`6^{((1)/(5) + (9)/(12) + (1)/(12) + (5)/(4))}`

=
`6^{((12 + 45 + 5 + 75)/(60))}`

{Since,
`a^(b) * a^(c) = a^((b + c))`}

=
`6^{(137)/(60)}`

=
`\sqrt[60]{6^(137) }` (Answer)