Easy Algebra Step-by-Step

Exponentiation 51

c. (.. 6 )−^2

Step 1. Write the reciprocal of the corresponding positive exponent version

of () 06. −^2.

2 1

() 06. =() 06. 2

−

Step 2. Evaluate () 06.^2.

1 1 1

036

2

()^06. =() 06. 2 =() 06. 6 () 060. =.

−

d.^3

4

⎛^3

⎝⎜

⎛⎛

⎝⎝

⎞

⎠⎟

⎞⎞

⎠⎠

−

Step 1. Write the reciprocal of the corresponding positive exponent version

of

3

4

3

⎛

⎝

⎛⎛⎛⎛

⎝⎝

⎛⎛⎛⎛ ⎞

⎠

⎞⎞⎞⎞

⎠⎠

⎞⎞⎞⎞

−

.

3

4

(^31)
3

⎛

⎝

⎛⎛⎛⎛

⎝⎝

⎛⎛⎛⎛ ⎞

⎠

⎞⎞⎞

⎠⎠

⎞⎞⎞⎞ =

() 34

−

Step 2. Evaluate

3

4

3

⎛

⎝

⎛⎛⎛⎛

⎝⎝

⎛⎛⎛⎛ ⎞

⎠

⎞⎞⎞

⎠⎠

⎞⎞⎞⎞ and simplify.

3

4

1 1

27 64

64

27

3

3

⎛

⎝

⎛⎛⎛⎛

⎝⎝

⎛⎛⎛⎛ ⎞

⎠

⎞⎞⎞

⎠⎠

⎞⎞⎞⎞ =

()^34

==

−

/

Notice that because x

x

n

n

− =^1 , the expression^1

x−n

can be simplifi ed as

follows:

11

xx 1 1

x

nn x

1

n

n

− === ; thus,

1

x

−n=xn. Apply this rule in the following

problem.

Problem Simplify.

a.^1

2 −^5

b.

1

() 2 −^5