EXPONENTS

EXPONENTS

EXPONENTS

When an expression appears to be x⁴ it means x.x.x.x or four times of x. It emplies that the x has four times itself. The x is the base and the small number four on the upper right part of the x is exponent.

In general:

Xⁿ = x . x. x. . . .n factors and it is the nth power of the base x.

Operation on terms with exponent.

The multiplication general form:

X ^m . X ⁿ = X ^m+n

This means we simply add the exponents when the two or more bases are multiplied.

Illustration:

1.           1.. (X² )(X³) = X ²⁺³ = X ⁵; where your m = 2 and n = 3

          

            2.       Y ⁶ Y⁴ = Y ⁶⁺⁴ = Y ¹⁰ ; what is your m and n?

3.       X ³ Y⁵ . X² = X ³⁺² .Y⁵ = X⁵ y⁵

4.       2².2³ = 2²⁺³ = 2⁵ = 2.2.2.2.2 = 32; in this case you base is 2.

5.       X³.X².X⁵ = X³⁺²⁺⁵ = X ¹⁰ ; you have three bases here, the three x.

Try to answer the following:

6.       M⁴.M⁵ =

7.       N⁴N⁵N² =

8.       2Y².3Y⁴ =

9.       2X¹.3X².4X⁴ =

10.       ax⁵.x2.bx =

^11.    x^-2.x^-3 = ( remember the + and – rule)

12.      2x⁵.-3x^-2 =

13.     -4y^-7.-y^-3.4y⁵ =

14      -5x².-xy² =

15       5xy.3xy.4xy =