# To Simplify This, Think in Terms of What the Exponents Mean

Exponent Review #1 September 26, 2012

Exponents: Exponents are shorthand for repeated multiplication of the same thing by itself. For example,

53=5∙5∙5=125

(-2)4=-2-2-2-2=16

x5=x∙x∙x∙x∙x

To simplify this, think in terms of what the exponents mean.

x3 means x∙x∙x

x4 means x∙x∙x∙x

Therefore, (x3)(x4) = (xxx)(xxxx)
= xxxxxxx
= x7

Note that x7 also equals x(3+4).

This demonstrates the first basic exponent rule.

RULE 1: Whenever you multiply two terms with the same base, you add the exponents: am∙an=am+n

èNote: We can NOT simplify (x4)(y3), because the bases are different: (x4)(y3) = xxxxyyy = (x4)(y3). Nothing combines.

Simplify the expressions below. If they cannot be simplified, write ‘Not Possible’.

1.  aaaaaa / 2.  -22 / 3.  -22
4.  x3z2 / 5.  x3x2x7 / 6.  x3y2y9
7.  x3y3z2 / 8.  x2y4x100y

To simplify this, think in terms of what the exponents mean.

x5=x∙x∙x∙x∙x

x2= x∙x

Therefore,

x5x2=xxxxxxx

=xxxxxxx=xxx=x3

Note that x3 also equals x(5−2). This demonstrates the second basic exponent rule.

RULE 2: Whenever you divide two terms with the same base, you can subtract the exponents:

aman=am-n

RULE 3: Anything to the power zero is just "1": a0=1

9.  -20 / 10. -20 / 11. x3 x2
12. x3z2 / 13. x3x12x4 / 14. x3y22y9
15. x3x0z2 / 16. x200y4x100y / 17. z5x
18. x0y0z0 / 19. x9y9z9x3yz0 / 20. z5z13

Some Information in this worksheet was obtained from :

Stapel, Elizabeth. "Fractional (Rational) Exponents." Purplemath. Available from

http://www.purplemath.com/modules/exponent5.htm. Accessed 22 April 2009Page 1