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Exponents

Problems

Properties of Exponents

Simplifying Expressions with Exponents

Problem : Are the following statements true sometimes, always, or never for a, b, c, d, k, l > 0 ?
a) (a + b)2 = a 2 + b 2
b) ca 2 + da 2 = (c + d )a 2
c) a k a l = a k+l
d) a k a l = a kl
e) (a k)l = a kl
f) a -2 < 1

a) Never.
b) Always.
c) Always.
d) Sometimes ( k = l = 2 , for example).
e) Always.
f) Sometimes.

Problem : 3x -4 -6x -4 = ?

-3x -4

Problem : 3x 2(5x 4) = ?

15x 6

Problem : = ?

x -2 or

Problem : (5x 2)4 = ?

625x 8

Problem : 5(3x)2 = ?

45x 2

Problem : 3x a(x 3) = ?

3x a+3

Problem : (2x 5)a

2a x 5 a

Problem : Write 256 and 1252 as quantities with a common base.

256 = 512 and 1252 = 56 .

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