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**

To find the value of the expression, if x= 4 what is ( x^-3/2) * ( x^100/ (x^99).

We know that putting the value x = in the expression directly and getting the value or putting the value of the expression after simplification are the same as the denominator is not zero for x = 4.

So let f(x) = ( x^-3/2) * ( x^100/ (x^99).

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

x^100/x^99 = x^(100-99) = x, as a^m/a^n = a^(m-n) by index law.

Therefore f(x) = {1/x^3/2)*x = x ^(1- 3/2) = x^(-1/2) = 1/x^(1/2) .

Therefore f(x) = 1/x^(1/2).

So at x = 4, f(x) = f(4) = 1/4^(1/2) = 1/2.

Therefore x^(-3/2)}(x^100)/(x^99) = 1/x^(1/2) = 1/2, for x= 4.