Exponents

Mathematics Review

Colleagues tell me that there are several topics from mathematics that probably need to be reviewed before you really get into problem solving. Try all of these. It is up to you to search out supplementary material when you find you need some additional revew.

Exponential Method of Expressing Numbers

For convenience in writing an manipulation, numbers are often expressed as factors of appropriate powers of 10.

¹²

1,969,000 = 1.969 * 10⁶

1,969 = 1.969 * 10³

.0001969 = 1.969 * 10^-4

Powers and Roots

^x+y

A^x / A^y = A^x-y

A⁰ = 1 (for A not equal to zero)

(AB)^x =A^xB^x

A^-x = 1/A^x

(A/B)^x = A^x/B^x

(A^x)^y = A^xy

A^x/y = the yth root of A^x

the xth root of the product AB = the xth root of A times the xth root of B

the xth root of the yth root of A = the xth times yth root of A

A^x/y = the yth root of A^x

the xth root of A/B = the xth root of A/the xth root of B

Problems

A³ * A⁴ = A⁴ * A³ -- True or False:
(-A)⁵ = -(A⁵)
(-A)² = -(A²)
A^x² = (A^x)²

When you have finished this section write me a short memo and tell me if you found this type of instruction helpful. Bring this to class sometime during the first two weeks of the course. 10 points extra credit.

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