What’s the least common multiple (lcm) for each group of numbers? a. 6 and 15 b. 4 and 11 c. 6, 9, and 12 d. 8, 10, and 20 what’s the least common denominator (lcd) for each group of fractions? a. 1⁄6 and 7⁄8 b. 3⁄4 and 7⁄10 c. 7⁄12, 3⁄8 and 11⁄36 d. 8⁄15, 11⁄30 and 3⁄5

LCM is least common multiple.

a. 6 and 15

6 = 2 x 3

15 = 3 x 5

LCM = 3 x 5 x 2 = 30

b. 4 and 11

4 = 2 x 2

11 = 1 x 11

LCM = 2 x 2 x 11 = 44

c. 6, 9, and 12

6 = 2 x 3

9 = 3 x 3

12 = 2 x 2 x 3

LCM = 2 x 2 x 3 x 3 = 36

d. 8, 10, and 20

8 = 2 x 2 x 2

10 = 2 x 5

20 = 2 x 2 x 5

LCM = 2 x 2 x 2 x 5 = 40

LCD is the least common denominator. Means we will find the LCM of denominators.

a. 1⁄6 and 7⁄8

6 = 2 x 3

8 = 2 x 2 x 2

LCD = 2 x 2 x 2 x 3 = 24

b. 3⁄4 and 7⁄10

4 = 2 x 2

10 = 2 x 5

LCD = 2 x 2 x 5 = 20

c. 7⁄12, 3⁄8 and 11⁄36

12 = 2 x 2 x 3

8 = 2 x 2 x 2

36 = 2 x 2 x 3 x 3

LCD = 2 x 2 x 2 x 3 x 3 = 72

d. 8⁄15, 11⁄30 and 3⁄5

15 = 3 x 5

30 = 2 x 3 x 5

5 = 1 x 5

LCD = 2 x 3 x 5 = 30

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

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step-by-step explanation: