Algebra Honors (Period 5 & 6)

Exponents 4-1
In the expression 5⁴ the number 4 is called the exponent and the number 5 is called the base
We call 5⁴ the exponential form of 5⋅5⋅5⋅5 (which is the expanded form)
The exponent tells you the number of times the base is used as a factor.
bⁿ = b⋅b⋅b⋅b⋅b⋅⋅⋅⋅b ( a total of n factors)
The expression bⁿ tells you that b is used as a factor n times.

-2⋅p⋅q⋅3⋅p⋅q⋅p written in exponential form is -6p³q²

Be careful when an expression contains both parentheses and exponents
(2y)³ = (2y)(2y)(2y) = 8y³
and
2y³ means 2⋅y⋅y⋅y = 2y³
-3⁴ = -81
(-3)⁴ = (-3)(-3)(-3)(-3) = +81
(1 + 5)² = 36
1 + 5²= 26
Simplify
(x –y)³/2x + y
for x = 2 and y = 5

-3

Simplify
x⁴ – a⁴
for x = 2 and a = 3
-65

[2³ + 3³] ÷ [2³ + (-1)²] = (8 + 27) /9 = 35/9


Evaluating terms - this is what we have been doing all year... plug it in, plug it in!!
Remember to ALWAYS put the number you substitute in parentheses!!

2x²y + 5xy - 4, where x = -4 and y = 5
Substitute carefully:

2(-4)²(5) + 5(-4)(5) - 4
= 2(16)(5) +(-20)(5) - 4
= 160 +(-100) -4
= 160 -104
= 56