Laws of Exponents. Exponential Notation Base Exponent Base raised to an exponent.
Exponent Law DescriptionAlgebraic representations To multiply powers with the same base, add the...
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Transcript of Exponent Law DescriptionAlgebraic representations To multiply powers with the same base, add the...
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