what is 3/x² in an indices form?

Question

i'm doing an exam style question but am getting lost with indices. I need 3/x² in an indices form so that i can go on to intergrate it.

indices form, as in all on one line. So, 1 / x would be x ^ -1

to clarify, i'm trying to find the intergration of 3 / x²

Answer 1

When there is a variable with power in denominator and you want to move the variable to the numerator, the power becomes exactly opposite to what it was in the denominator... if the power was negative in denominator, after moving the variable to numerator the power will be positive... if the power was positive in denominator, after moving the variable to numertor the power will be negative... it also applies to numbers, not just variables... in mathematical terms, it can be shown as...

1/ a^m can be rewritten as a^(-m)...
a^m can be rewritten as 1/a^-m...

so 3/x^2 = 3 * x^-2

∫ 3 * x^-2 dx = { [3 * x^(-2+1)]/(-2+1) } + c... remember the power rule...

∫ 3 * x^-2 dx = { [3 * x^(-2+1)]/(-2+1) } + c = ( -3/x ) + c

Answer 2

3/x^2 =3 * x^-2 =3 x^ -2

Answer 3

Note that
1/X may be written as X^(-1)
1/X^2 may be written as X^(-2)
1/X^3 may be written as X^(-3) etc
3/X^2= 3 x 1/X^2= 3 x X^(-2 ) = 3X^(-2)
Integral is -3/X

Answer 4

3/x^2 in an indices form is 3x^(-2)

Answer 5

3/x² can be rewritten as
3x-²
the integral of (3x-²)dx
=3*integral (x-²)dx
= -3/x+C,
where C is a constant

you will need to do more work
on indices when going into the
more advanced levels of
integration

i hope that this helps

Answer 6

3 times x to the power of -2.( Can't get indeces on this da*n keyboard.

x to power -1 = 1/x

Answer 7

not its u ARE U ******* Tthick U CNUT
3X^2 integrated is 6x

as 3 x 2 =6 and 2-1 =1 therfor 6x^1 or 6x

6x

don't answer if u don't know u thick knob tosser

Answer 8

My ability with computers isn't great, but let me put it this way...

if we say that x(2) means x to the power of 2,
then x(-2) is 1/(x(2)).
Thus the relevant index is
-2.

Answer 9

let say;
f(x)= 3/x^2 = 3x^(-2)
f'(x)= -6x^(-3)
= -6/x^3

Answer 10

algebra ... never understood it!