Easy Algebra Step-by-Step

(Marvins-Underground-K-12) #1

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
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