# 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

Example 1: Simplify (x3)(x4) Copyright © Elizabeth Stap999-2009 All Rights Reserved

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’.**

4. x3z2 / 5. x3x2x7 / 6. x3y2y9

7. x3y3z2 / 8. x2y4x100y

Example 2: Simplify x5x2Copyright

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

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