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Problems

Problems

Problem : Are the following statements true sometimes, always, or never for a, b, c, d, k, l > 0?
a) (a + b)2 = a2 + b2
b) ca2 + da2 = (c + d )a2
c) akal = ak+l
d) akal = akl
e) (ak)l = akl
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 : 3x2(5x4) =?

15x6

Problem : =?

x-2 or

Problem : (5x2)4 =?

625x8

Problem : 5(3x)2 =?

45x2

Problem : 3xa(x3) =?

3xa+3

Problem : (2x5)a

2ax5a

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

256 = 512 and 1252 = 56.