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An exponent is shorthand to write repeated
multiplication.
Example:
A · A · A · A
can be written:
A4
Example:
A
can be written:
A1
however, it is customary not to show the 1, it
is implied.
Zero Exponent reduces its argument
to 1.
Example:
B0
= 1
A negative exponent means to write
the reciprocal and change the exponent to a
positive
Examples:
C-1
= 1/C
D-3
= 1/D3
(which equals 1 /(D · D · D) )
1/T-2
= T2
The exponent applies to the base only as
shown in this next example.
Here is an example where the exponent
applies to a grouping of terms.
A fractional exponent means a root
of the base.
Examples:
G1/2
= √2
"the square root of G"
H1/5
= 5√H
"the 5th root of H"
Example:
A2/3
= (A1/3)2
= (A2)1/3
'the cube root of A then squared or A
squared then cube root"
Rules
for exponents.
An A is called the base and n is the
exponent.
Addition/Subtraction:
Only when
the bases are equal and the exponents are equal can the
numbers be added or subtracted.
Example:
53 + 53 = 2x53
Example:
A4 + 3xA4 = 4xA4
Example:
2B2 – B2 = B2
Example:
5C3 + C5 =
exponents are different, cannot combine
Multiplication/Division:
Only
exponents with the same base can be multiplied
or divided.
1) Am
x An = Am+n
Example:
A3 x A4 = A3+4 = A7
Example:
B2 x C3 x B3 x A4
x C = B2+3 x C3+1 x A4 = B5
x C4 x A4
2) Am
/ An = Am-n
Example:
A6 / A3 = A6-3 = A3
3) (Am)n
= Amxn = Amn
(An)m
= Anxm = Anm
Example:
(A4)3 = A4x3 = A12
Applying
these rules in algebraic
expressions can be challenging. What you need to remember
is, working with fractions, the
numerator and denominator must each be products of
terms, and the bases you combine must be the same.
Download
our free math lesson plan template...and print!!
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