Exponents:
In Online algebra 1 help exponents are very important
In ab, a is the base and b is the exponent. The exponent tells us how many times the base is used as factor.
ab = a.a.a………………..a(b factors of a)
for example 42, in this 4 is base and 2 is exponent and 4 is multiplied 2 times 4x4=16.
Rules of Exponents:
1) Am x An = Am+n
2) Am / An = Am-n
3) (Am)n = Amn
4) A0 = 1
5) A-1 = 1/A
6) (AB)m = Am Bm
7) (A/B)m = Am / Bm
Points to remember:
0n = 0; if n is positive
0n = undefined; if n is negative because it becomes 1/0n which is undefined.
Problems on Exponents
Here is few free algebra 1 answers on exponents .
Example 1: Simplify [(3x4 y2 z8)/(x3 y z2)]0
Solution : The answer is 1. There is no need to solve because there is power of 0 of whole expression. If we consider (3x4 y2 z8)/(x3 y z2) = A then this expression becomes A0 which is equal to 1.
Example 2: Determine 242 / 34
Solution: 242 / 34 = (8 x 3)2 / 34
= 82 x 32/34
= 82/32
= 64/9
Roots
Roots are the inverse of exponents. The nth root of a number is written as:
$$\sqrt[n]{a}$$
Where n is index, x is radicand and ? is radical.
Example: find the value of $$\sqrt[3]{64}$$
Solution: = (64)(1/3)
= {(4)3}1/3
= (4)3x1/3
= (4)1 = 4
Square Root
The square root is the inverse of squaring. Every positive number has two square root on is positive and one is negative. For example 2 and -2 both are the square roots of 4.
Properties :
- ?(a+b) ? ?a + ?b
- ?(ab) = ?a ?b
- ?(a/b) = ?a /?b
Related Tags
Explain Exponents And Roots , Notes on Exponents And Roots , What is Exponents And Roots