If x= 2. Find x^2/3 ( x^120/ x^110) * x^-7 ?

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hala718 | High School Teacher | (Level 1) Educator Emeritus

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Given x = 2.

Let E (x) =  x^2/3 ( x^120/ x^110) * x^-7

Then, we need to calculate E(2).

First, let us simplify the expression.

x^2/3 ( x^120 / x^110) * x^-7

Let us simplify between the brackets.

( x^120/ x^110)

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

==> x^120/ x^110 = x^(120-110)= x^10

==> E(x) = (x^2/3) ( x^10) * x^-7

Now we know that x^a* x^b =x^ (a+b).

==> E(x) = x^ ( 2/3 + 10 + -7)

                = x^ (2/3 + 3)

                 = x^(11/3).

==> E(x) = x^ 11/3

Now let us substitute with x= 2.

==> E(2) = 2^11/3 = 12.7 ( approx.)

Then E (x) = 12.7  when x = 2.

 

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neela | High School Teacher | (Level 3) Valedictorian

Posted on

If x= 2. Find x^2/3 ( x^120/ x^110) * x^-7 .

We see that f(2) is not indeterminate for x= 2.

So f(x) = x^120/x^110 could be simplified first and then we can put x = 2.

Therefore f(x) = x^120/x^110

f(x)= {x^(110+10)}/x^110 .  But a^(m+n) = a^m*a^n by exponent law.

f(x) = x^110}*x^10/x^110.

f(x) = x^10.

No w put x = 2  in f(x) = x^10.

f(2) = 2^10.

f(2) = 1024.

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