Easy Algebra Step-by-Step

56 Easy Algebra Step-by-Step

Problem Evaluate using xm//n ()xm n.

a. ⎛−

⎝⎜

⎛⎛

⎝⎝

⎞

⎠⎟

⎞⎞

⎠⎠

1

8

23 /

b. ()^32 //

Solution

a. ⎛−

⎝⎜

⎛⎛

⎝⎝

⎞

⎠⎟

⎞⎞

⎠⎠

1

8

23 /

Step 1. Rewrite ⎛−

⎝

⎛⎛⎛⎛

⎝⎝

⎛⎛⎛⎛ ⎞

⎠

⎞⎞⎞⎞

⎠⎠

(^1) ⎞⎞⎞⎞
8
23 /
using xm//n ()xm n.

⎛−

⎝

⎛⎛⎛⎛

⎝⎝

⎛⎛⎛⎛ ⎞

⎠

⎞⎞⎞⎞

⎠⎠

⎞⎞⎞⎞ =−⎛

⎝

⎛⎛

⎝⎝

⎞

⎠

⎞⎞⎞⎞

⎠⎠

⎡ ⎞⎞⎞⎞

⎣

⎢

⎡⎡

⎣⎣

⎤

⎦

⎥

⎤⎤

⎦⎦

1

8

1

8

23 / 2 13 /

Step 2. Find ⎛−

⎝

⎛⎛⎛⎛

⎝⎝

⎛⎛⎛⎛ ⎞

⎠

⎞⎞⎞⎞

⎠⎠

(^1) ⎞⎞⎞⎞
8
2
.

⎝⎝⎛⎛⎛⎝⎛⎛⎛⎛⎛⎛− ⎞⎠⎞⎞⎞⎞⎠⎠⎞⎞⎞⎞ =

1

8

1

64

2

Step 3. Find

1

64

13

⎡

⎣⎢

⎡⎡

⎣⎣

⎤

⎦⎥

⎤⎤

⎦⎦

/

.

1

64

1

4

13

⎡

⎣⎢

⎡⎡

⎣⎣

⎤

⎦⎥

⎤⎤

⎦⎦

=

/

Step 4. Review the main results.

⎛−

⎝

⎛⎛⎛⎛

⎝⎝

⎛⎛⎛⎛ ⎞

⎠

⎞⎞⎞⎞

⎠⎠

⎞⎞⎞⎞ =−⎛

⎝

⎛⎛

⎝⎝

⎞

⎠

⎞⎞⎞⎞

⎠⎠

⎡ ⎞⎞⎞⎞

⎣

⎢

⎡⎡

⎣⎣

⎤

⎦

⎥

⎤⎤

⎦⎦

=⎡

⎣⎢

⎡⎡

⎣⎣

⎤

⎦⎥

⎤⎤

⎦⎦

=

1

8

1

8

1

64

1

4

23 / 2 13 / 13 /

b. ()^32 //

Step 1. Rewrite () 3632 / using xm//n ()xm n.

() 3632 / =() 3636313 /^2