If x= 4 what is ( x^-3/2) * ( x^100/ (x^99) ?

If x= 4  what is ( x^-3/2) * ( x^100/
(x^99)

Let E(x) = (x^-3/2) * ( x^100/
(x^99)

First we will simplify the
expression.

Let us review the exponent's
properties.

We know
that:

x^(-a) =
1/(x^a)

==> E(x) = 1/(x^3/2)] * ( x^100 /
x^99)

Now we will simplify x^100 /
x^99

We know that x^a/x^b = x^(a-b)
.

==> x^100/ x^99= x^(100-99) = x^1 =
x

==> E(x) = 1/(x^3/2)  *
x

                = x/
(x^3/2)

                 = x^1 /
(x^3/2)

                  = x^(1 -
3/2)

                  =
x^(-1/2)

                    =
1/(x^1/2)

                  =
1/sqrtx

==> E(x) =
1/sqrtx

Then the final simple form for E(x) is
1/sqrtx.

Now given x=
4.

==> E(4) = 1/ sqrt4 = 1/
2

==> (x^-3/2 ) * ( x^100/ x^99) =
1/2