Question

Type the correct answer in the box. simplify this expression ​

Answer 1

The solution to the expression after simplifying it is
`(mn)/(3)`

Simplification of indices.

In mathematics, indices is a way of writing a repeated multiplicated number as a power or exponent form. The simplification of indices involves the appropriate use of the rules of exponents to simplify the indices into their simplest form.

From the given information, we are to simplify;

`((m^5n^5)^(1/6))/(3(mn)^(-1/6))`

Using the power rule;

`((m^(5*1/6)n^(5*1/6)))/(3(m^(-1/6)n^(-1/6)))`

`((m^(5/6)n^(5/6)))/(3(mn)^(-1/6))`

Division changes to subtraction when subtracting indices with the same base; i.e.

`((m^(5/6-(-1/6))n^(5/6-(-1/6))))/(3)`

`((m^(5/6+1/6)n^(5/6+1/6)))/(3)`

`((m^(6/6)n^(6/6)))/(3)`

`(mn)/(3)`

Answer 2

a)
`(1)/(3) m n`

Explanation:

Explanation:-

Given expression

=
`(\frac{(m^5 n^5)^{(1)/(6) } }{3 (mn)^{(-1)/(6) } } )`

we will apply formula

(ab)ⁿ = aⁿ b ⁿ

=
`(\frac{(m^5 n^5)^{(1)/(6) } }{3(m)^{(-1)/(6) } (n)^{(-1)/(6) } } )`

=
`(1)/(3) m^{(5)/(6) } n^{(5)/(6) } m^{(1)/(6) } n^{(1)/(6) }`

base terms are equal then powers will be add

=
`(1)/(3) m^{(5+1)/(6) } n^{(5+1)/(6) }`

=
`(1)/(3) m^(1) n^{\frac{1}`

=
`(1)/(3) m n`