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Exponent Law DescriptionAlgebraic representations To multiply powers with the same base, add the exponents n a x n b = n a+b To divide powers with the same base, subtract the exponents n a n b = n a-b
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Exponent Law Description Algebraic representations
To multiply powers with To multiply powers with the same base, add the the same base, add the
exponentsexponents
nnaa x n x nbb = n = na+ba+b
Exponent Law Description Algebraic representations
To multiply powers with To multiply powers with the same base, add the the same base, add the
exponentsexponents
nnaa x n x nbb = n = na+ba+b
To divide powers with To divide powers with the same base, subtract the same base, subtract
the exponentsthe exponents
nnaa n nbb = n = na-ba-b
Exponent Law Description Algebraic representations
To multiply powers with To multiply powers with the same base, add the the same base, add the
exponentsexponents
nnaa x n x nbb = n = na+ba+b
To divide powers with To divide powers with the same base, subtract the same base, subtract
the exponentsthe exponents
nnaa n nbb = n = na-ba-b
To determine the power To determine the power of a power multiply the of a power multiply the exponentsexponents
(n(naa))bb = n = nabab
Exponent Law Description Algebraic representations
The power of a product The power of a product is equal to the product is equal to the product
of the powersof the powers
(m x n)(m x n)aa = m = maa x n x naa
Exponent Law Description Algebraic representations
The power of a product The power of a product is equal to the product is equal to the product
of the powersof the powers
(m x n)(m x n)aa = m = maa x n x naa
The power of a quotient The power of a quotient is equal to the quotient is equal to the quotient
of the powersof the powers
mn( )a
=ma
na
Exponent Law Description Algebraic representations
The power of a product The power of a product is equal to the product is equal to the product
of the powersof the powers
(m x n)(m x n)aa = m = maa x n x naa
The power of a quotient The power of a quotient is equal to the quotient is equal to the quotient
of the powersof the powers
Zero exponentZero exponent xx00 = 1, x = 1, x00
mn( )a
=ma
na
Exponent Law Description Algebraic representations
The power of a product The power of a product is equal to the product is equal to the product
of the powersof the powers
(m x n)(m x n)aa = m = maa x n x naa
The power of a quotient The power of a quotient is equal to the quotient is equal to the quotient
of the powersof the powers
Zero exponentZero exponent xx00 = 1, x = 1, x00Negative ExponentsNegative Exponents xx-n-n = =
mn( )a
=ma
na
1xn
(4x3y2)(5x2y4)
Solution
(4x3y2)(5x2y4) means 4 * x3 * y2 * 5 * x2 * y4
We can multiply in any order.
(4x3y2)(5x2y4) = 4 * 5 * x3 * x2 * y2 * y4
= 20x5y6
Solution
6a5b3
3a2b2
6a5b3
3a2b2means 6
3a5
a2b3
b2x x
= 63
a5
a2b3
b2x x6a5b3
3a2b2
= 22aa33bb
Solution
means x2
z3x2
z3*
=
=
x2
z3(( ))22
x2
z3(( ))22
x2
z3(( ))22 xx22
zz33xx22
zz33*
xx44
zz66
c-3 * c5
Solution
c-3 * c5 = c-3+5
Same methods apply if Same methods apply if some of the exponents are some of the exponents are negative integersnegative integers
= c2
m2 * m-3
Solution
m2 * m-3 = m2 +(-3)
Same methods apply if Same methods apply if some of the exponents are some of the exponents are negative integersnegative integers
= m-1
(a-2)-3
Solution
(a-2)-3 = a(-2)(-3)
Same methods apply if Same methods apply if some of the exponents are some of the exponents are negative integersnegative integers
= a6
Remember exponent Remember exponent law #2law #2
( power of powers)( power of powers)
(3a3b-2)(15a2b5)
Solution
(3a3b-2)(15a2b5) means 3* 15 * a3 * a2 * b-2 * b5
We can multiply in any order.
Same methods apply if Same methods apply if some of the exponents are some of the exponents are negative integersnegative integers
(3a3b-2)(15a2b5) = 3* 15 * a3 * a2 * b-2 * b5
= 45a5b3
Solution
42x-1y4
7x3y-2
means 42 7
X-1
x3y4
y-2x x
=
= 66xx-4-4yy66
42x-1y4
7x3y-2
42x-1y4
7x3y-242 7
X-1
x3y4
y-2x x
= 6y6
x4 Positive ExponentsPositive Exponents
Same methods apply if Same methods apply if some of the exponents are some of the exponents are negative integersnegative integers
(a-3b2)3
Solution
(a-3b2)3 means a(-3)(3) * b(2)(3)
(a-3b2)3 = a(-3)(3) * b(2)(3)
= a-9b6
= b6
a9 Positive ExponentsPositive Exponents
Same methods apply if Same methods apply if some of the exponents are some of the exponents are negative integersnegative integers
CLASSWORK• PAGE 294• #3-8• #9 (e,f,g,h,I,j)• #10 – 13
• Page 295• #18, #20