SOLUTION: What do Laws of Exponent means? Explain and give some examples.

Question 463067: What do Laws of Exponent means?
Explain and give some examples.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
these are the laws that i know of.
law number 1
x^0 = 1
this means that any number raised to the power of 0 is equal to 1.
law number 2
x^1 = x
this means that any number raised to the power of 1 is equal to the number.
law number 3
x^2 = x*x (x is multiplied by x 1 time)
x^3 = x*x*x (x is multiplied by x 2 times)
x^4 = x*x*x*x (x is multiplied by x 3 times)
in general x^n means that x is multiplied by x (n-1) times.
law number 4
a^b * a^c = a^(b+c)
example:
2^2 + 2^3 = 2^(2+3) = 2^5 = 32.
proof:
2^2 = 4 and 2^3 = 8 and 4*8 = 32.
law number 5
a^b / a^c = a^(b-c)
example:
2^3 / 2^2 = 2^(3-2) = 2^1 = 2
proof:
2^3 = 8 and 2^2 = 4 and 8/4 = 2
law number 6
(a^b)^c = a^(b*c)
example:
(2^2)^3 = 2^6 = 64
proof:
2^2 = 4 and 4^3 = 64
law number 7
a^(-b) = 1/(a^b)
example:
2^(-3) = 1/(2^3) = 1/8
proof:
use your calculator to derive 2^(-3) and you will get an answer of .125
use your calculator to derive 1/(2^3) and you will also get an answer of .125.
law number 8
a^(1/b) = the bth root of a
example:
64^(1/6) = = 2
proof:
use your calculator to derive 64^(1/6) and you will get an answer of 2.
use your calculator to derive and you will also get an answer of 2.
law number 9
(a*b)^c = a^b * a^c
example:
(2*5)^3 = 2^3 * 5^3 = 8 * 125 = 1000
proof:
2*5 = 10 and 10^3 = 1000
law number 10
(a/b)^c = a^c / b^c
example:
(10/5)^3 = 10^3 / 5^3 = 1000 / 125 = 8
proof:
(10/5)^3 = 2^3 = 8
these are all i can remember off the top of my head.
they should cover all or most of the exponent laws you will encounter.
search the web for tutorials on "laws of exponents" and you will discover a wealth of material that you can reference.

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