Algebra I –Wilsen
Unit 5: Exponents
Day One
BLOCK 2
Exponents
A power is an expression like the following:
23
This power is read: “2 cubed” or “2 to the 3rd power”.
Example 1
Write out the meaning of each power expression, then evaluate.
23 = 2 2 2 =
42 = ____________ = ______
“4 squared” or “4 to the 2nd power”
54 = ____________ = ______
“5 to the 4th power”
Example 2
Be careful with negative signs! Compare the following two
expressions:
(–2)4 = _______________ = ______ Everything in ( ) is multiplied!
–24 = ________________ = ______ Take the opposite of the answer.
Example 3
Again, compare the following two expressions:
(–4)2 = _______________ = ______ Everything in ( ) is multiplied!
–42 = ________________ = ______ Take the opposite of the answer.
Now let’s consider variables!
Example 4
Write each expression as a power:
x x x = ________
y y = ________
2 x x x x y y y = ________
2 2 • 3 • 3 • 3 • x x x x y y y = ________
If a variable does not have an exponent, the exponent is actually ______.
Example 5
Evaluate –2 2 – 4 ( –3) – 2 ( –2 ) – 2
3
2
Write each of these out the long way, and then evaluate. Be careful with negative signs!
1.
32
2.
53
3.
42
4.
(–5)2
5.
(–2)3
6.
(–3)2
7.
(–2)4
8.
63
9.
–4 2
Rewrite each of these with exponents, and parentheses if necessary.
10. – 3 • –3 • –3
11. –3 • 3 • 3
Evaluate each of these, following the order of operations.
12. –32 – ( –3) + ( –2 )
2
2
13. –2 2 – 4 ( –3) – 2 ( –2 ) – 2
3
14. ( –2 ) ( 5 ) ( –3)
3
3
2
16. ( –3) ( 2 4 ) x 2
18.
( –2 )4 x • 2x 2
2
2
15. 5 2 ( –2 )
3
17. ( xy )( 4xy )