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