WORKED EXAMPLE 11 Simplify by using index notation where appropriate
Simplify:
a. 2xk
THINK
b. 3x2k
c. k x 2kx
d. 3kx2k
WRITE
a. 2Xk
= 2k
6k
C. kX2XkXA
= 2 x k2xx
= 2k2:r
d. 3XkX2Xk
= 6k2
e. 3k x 2k2X
2.
3.
2.
3.
2.
3.
2.
3.
The coefficient of a pronumeral represents multiples of
the pronumeral.
Remove the multiplication sign.
Rewrite in expanded form.
Multiply the numbers.
Remove the multiplication sign.
Rewrite in expanded form.
Write pronumerals with index.
Remove the multiplication sign.
Rewrite in expanded form.
Multiply the numbers and write pronumerals with index.
Remove the multiplication sign.
Rewrite in expanded form.
Multiply the numbers and •write pronumerals With index.
Remove the multiplication sign.
e.
3xkx2xkxkxx
= 6k^3
To simplify the expression, we can follow these steps:
a. 2xk
The coefficient of a pronumeral represents multiples of the pronumeral. In this case, the coefficient of k is 2.
Remove the multiplication sign.
2k
Rewrite in expanded form.
2k
Therefore, the simplified form of 2xk is 2k.
b. 3x2k
The coefficient of a pronumeral represents multiples of the pronumeral. In this case, the coefficient of k is 2.
Remove the multiplication sign.
3 x 2k
Rewrite in expanded form.
6k
Therefore, the simplified form of 3x2k is 6k.
c. k x 2kx
The coefficient of a pronumeral represents multiples of the pronumeral. In this case, the coefficient of k is 2.
Remove the multiplication sign.
k x 2k x k
Multiply the numbers and write pronumerals with index.
2 x k^2
Therefore, the simplified form of k x 2kx is 2k^2.
d. 3kx2k
The coefficient of a pronumeral represents multiples of the pronumeral. In this case, the coefficient of k is 2.
Remove the multiplication sign.
3k x 2k
Rewrite in expanded form.
6k^2
Therefore, the simplified form of 3kx2k is 6k^2.
e. 3k x 2k^2
The coefficient of a pronumeral represents multiples of the pronumeral. In this case, the coefficient of k is 2.
Remove the multiplication sign.
3k x 2k^2
Multiply the numbers and write pronumerals with index.
6k^3
Therefore, the simplified form of 3k x 2k^2 is 6k^3.