Fractional indices pls help me

Question

asked Apr 16, 2022 191k views

1 Answer

Julius Bullinger · Answer 1 · 2022-04-23T17:20:35+0000

Answer:

(7)/(4) x²

Explanation:

Dealing with the numerical part

(7)/(8) ÷
(1)/(2) =
(7)/(8) ×
(2)/(1) =
(14)/(8) =
(7)/(4)

Using the rule of exponents

(a^(m) )/(a^(n) ) =
a^((m-n)) , then

$\frac{x^{(1)/(2) } }{x^{-(3)/(2) } }$

=
$x^{((1)/(2)-(-(3)/(2)) }$

=
$x^{((1)/(2)+(3)/(2)) }$

=
$x^{(4)/(2) }$

= x²

Then

(7)/(8)
$x^{(1)/(2) }$ ÷
(1)/(2)
$x^{-(3)/(2) }$

=
(7)/(4) x²