<< Chapter < Page Chapter >> Page >

Simplify: ( 16 m 1 3 ) 3 2 ( 81 n 2 5 ) 3 2 .

64 m 1 2 729 n 3 5

Got questions? Get instant answers now!

Simplify: ( m 3 n 9 ) 1 3 ( p 4 q 8 ) 1 4 .

Solution


  1. ( m 3 n 9 ) 1 3 First we use the Product to a Power Property. ( m 3 ) 1 3 ( n 9 ) 1 3 To raise a power to a power, we multiply the exponents. m n 3


  2. ( p 4 q 8 ) 1 4 First we use the Product to a Power Property. ( p 4 ) 1 4 ( q 8 ) 1 4 To raise a power to a power, we multiply the exponents. p q 2
Got questions? Get instant answers now!
Got questions? Get instant answers now!

We will use both the Product and Quotient Properties in the next example.

Simplify: x 3 4 · x 1 4 x 6 4 y 4 3 · y y 2 3 .

Solution


  1. x 3 4 · x 1 4 x 6 4 Use the Product Property in the numerator, add the exponents. x 2 4 x 6 4 Use the Quotient Property, subtract the exponents. x 8 4 Simplify. x 2


  2. y 4 3 · y y 2 3 Use the Product Property in the numerator, add the exponents. y 7 3 y 2 3 Use the Quotient Property, subtract the exponents. y 9 3 Simplify. y 3
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Simplify: m 2 3 · m 1 3 m 5 3 n 1 6 · n n 11 6 .

m 2 n 3

Got questions? Get instant answers now!

Simplify: u 4 5 · u 2 5 u 13 5 v 1 2 · v v 7 2 .

u 3 v 5

Got questions? Get instant answers now!

Key concepts

  • Summary of Exponent Properties
  • If a , b are real numbers and m , n are rational numbers, then
    • Product Property a m · a n = a m + n
    • Power Property ( a m ) n = a m · n
    • Product to a Power ( a b ) m = a m b m
    • Quotient Property :
      a m a n = a m n , a 0 , m > n
      a m a n = 1 a n m , a 0 , n > m
    • Zero Exponent Definition a 0 = 1 , a 0
    • Quotient to a Power Property ( a b ) m = a m b m , b 0

Practice makes perfect

Simplify Expressions with a 1 n

In the following exercises, write as a radical expression.


x 1 2
y 1 3
z 1 4

Got questions? Get instant answers now!


r 1 2
s 1 3
t 1 4

r s 3 t 4

Got questions? Get instant answers now!


u 1 5
v 1 9
w 1 20

Got questions? Get instant answers now!


g 1 7
h 1 5
j 1 25

g 7 h 5 j 25

Got questions? Get instant answers now!

In the following exercises, write with a rational exponent.


x 7
y 9
f 5

Got questions? Get instant answers now!


r 8
.
t 4

r 1 8 s 1 10 t 1 4

Got questions? Get instant answers now!


u 5
v
.

u 1 5 v 1 2 w 1 16

Got questions? Get instant answers now!


7 c 3
12 d 7
3 5 f 4

Got questions? Get instant answers now!


5 x 4
9 y 8
7 3 z 5

( 5 x ) 1 4 ( 9 y ) 1 8 7 ( 3 z ) 1 5

Got questions? Get instant answers now!


21 p
8 q 4
4 36 r 6

Got questions? Get instant answers now!


25 a 3
3 b
.

( 25 a ) 1 3 ( 3 b ) 1 2 ( 40 c ) 1 10

Got questions? Get instant answers now!

In the following exercises, simplify.


81 1 2
125 1 3
64 1 2

Got questions? Get instant answers now!


625 1 4
243 1 5
32 1 5

5 3 2

Got questions? Get instant answers now!


16 1 4
16 1 2
3125 1 5

Got questions? Get instant answers now!


216 1 3
32 1 5
81 1 4

6 2 3

Got questions? Get instant answers now!


( −216 ) 1 3
216 1 3
( 216 ) 1 3

Got questions? Get instant answers now!


( −243 ) 1 5
243 1 5
( 243 ) 1 5

−3 −3 1 3

Got questions? Get instant answers now!


( −1 ) 1 3
−1 1 3
( 1 ) 1 3

Got questions? Get instant answers now!


( −1000 ) 1 3
1000 1 3
( 1000 ) 1 3

−10 −10 1 10

Got questions? Get instant answers now!


( −81 ) 1 4
81 1 4
( 81 ) 1 4

Got questions? Get instant answers now!


( −49 ) 1 2
49 1 2
( 49 ) 1 2

not a real number −7 1 7

Got questions? Get instant answers now!


( −36 ) 1 2
36 1 2
( 36 ) 1 2

Got questions? Get instant answers now!


( −1 ) 1 4
( 1 ) 1 4
1 1 4

not a real number 1 −1

Got questions? Get instant answers now!


( −100 ) 1 2
100 1 2
( 100 ) 1 2

Got questions? Get instant answers now!


( −32 ) 1 5
( 243 ) 1 5
125 1 3

−2 1 3
−5

Got questions? Get instant answers now!

Simplify Expressions with a m n

In the following exercises, write with a rational exponent.


m 5
n 2 3
p 3 4

Got questions? Get instant answers now!


r 7 4
s 3 5
t 7 3

r 7 4 s 3 5 t 7 3

Got questions? Get instant answers now!


u 2 5
v 8 5
w 4 9

Got questions? Get instant answers now!


a 3
b 5
c 5 3

a 1 3 b 1 5 c 5 3

Got questions? Get instant answers now!

In the following exercises, simplify.


16 3 2
8 2 3
10,000 3 4

Got questions? Get instant answers now!


1000 2 3
25 3 2
32 3 5

100 125 8

Got questions? Get instant answers now!


27 5 3
16 5 4
32 2 5

Got questions? Get instant answers now!


16 3 2
125 5 3
64 4 3

64 3125 256

Got questions? Get instant answers now!


32 2 5
27 2 3
25 3 2

Got questions? Get instant answers now!


64 5 2
81 3 2
27 4 3

32,768 1 729 1 81

Got questions? Get instant answers now!


25 3 2
9 3 2
( −64 ) 2 3

Got questions? Get instant answers now!


100 3 2
49 5 2
( −100 ) 3 2

1000 1 16,807 not a real number

Got questions? Get instant answers now!


9 3 2
9 3 2
( −9 ) 3 2

Got questions? Get instant answers now!


64 3 2
64 3 2
( −64 ) 3 2

−512
1 512 not a real number

Got questions? Get instant answers now!


100 3 2
100 3 2
( −100 ) 3 2

Got questions? Get instant answers now!


49 3 2
49 3 2
( −49 ) 3 2

−343 1 343 not a real number

Got questions? Get instant answers now!

Use the Laws of Exponents to Simplify Expressions with Rational Exponents

In the following exercises, simplify.


4 5 8 · 4 11 8
m 7 12 · m 17 12
p 3 7 · p 18 7

Got questions? Get instant answers now!


6 5 2 · 6 1 2
n 2 10 · n 8 10
q 2 5 · q 13 5

216 n q 3

Got questions? Get instant answers now!


5 1 2 · 5 7 2
c 3 4 · c 9 4
d 3 5 · d 2 5

Got questions? Get instant answers now!


10 1 3 · 10 5 3
x 5 6 · x 7 6
y 11 8 · y 21 8

100 x 2 y 4

Got questions? Get instant answers now!


( m 6 ) 5 2
( n 9 ) 4 3
( p 12 ) 3 4

Got questions? Get instant answers now!


( a 12 ) 1 6
( b 15 ) 3 5
( c 11 ) 1 11

a 2 b 9
c

Got questions? Get instant answers now!


( x 12 ) 2 3
( y 20 ) 2 5
( z 16 ) 1 16

Got questions? Get instant answers now!


( h 6 ) 4 3
( k 12 ) 3 4
( j 10 ) 7 5

h 8 k 9 j 14

Got questions? Get instant answers now!


x 7 2 x 5 2
y 5 2 y 1 2
r 4 5 r 9 5

Got questions? Get instant answers now!


s 11 5 s 6 5
z 7 3 z 1 3
w 2 7 w 9 7

s z 2 1 w

Got questions? Get instant answers now!


t 12 5 t 7 5
x 3 2 x 1 2
m 13 8 m 5 8

Got questions? Get instant answers now!


u 13 9 u 4 9
r 15 7 r 8 7
n 3 5 n 8 5

u r 1 n

Got questions? Get instant answers now!


( 9 p 2 3 ) 5 2
( 27 q 3 2 ) 4 3

Got questions? Get instant answers now!


( 81 r 4 5 ) 1 4
( 64 s 3 7 ) 1 6

3 r 1 5 2 s 1 14

Got questions? Get instant answers now!


( 16 u 1 3 ) 3 4
( 100 v 2 5 ) 3 2

Got questions? Get instant answers now!


( 27 m 3 4 ) 2 3
( 625 n 8 3 ) 3 4

9 m 1 2 125 n 2

Got questions? Get instant answers now!
Practice Key Terms 1

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elementary algebra' conversation and receive update notifications?

Ask