Question

Apply the properties of exponents to rewrite each expression in the form kkxxnn, where nn is an integer and x ≠0

(x^2/4x^−1)^−3

Answer 1

`64x^(-9)`

Explanation:

Here, in this given problem, we have to apply the properties of indices or properties of exponents to write the following expression
`((x^(2) )/(4x^(-1) )) ^(-3)`

in the form kkxxnn, where nn is an integer and x ≠ 0.

Now,
`((x^(2) )/(4x^(-1) )) ^(-3)`

=
`((x^(2-(-1)) )/(4) )^(-3)`

{Since we know the property of exponent
`(x^(a) )/(x^(b) ) =x^((a-b))`}

=
`((x^(3) )/(4)) ^(-3)`

=
`((4)/(x^(3) ) )^(3)`

{Since we know the property of exponent
`x^(-a)= (1)/(x^(a) )`}

=
`(64)/(x^(3*3) )`

{Since we know the property of indices
`(x^(a)) ^(b) =x^(ab)`}

=
`64x^(-9)` (Answer)