SOLUTION: Explain why -5x� and (-5x)� are not equivalent. Explain why the expressions 2� � 5� and 10� are equivalent.

Question 630183: Explain why -5x� and (-5x)� are not equivalent.
Explain why the expressions 2� � 5� and 10� are equivalent.
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Important: Exponents only apply to what is literally in front of them!

In it is the "x" that is in front of the exponent. So the exponent applies only to the x. So is short for .

In it is the right parenthesis that is in front of the exponent. This means that the exponent applies to the whole expression inside the parentheses. So is short for (which simplifies to ).

One of the rules/properties of exponents is:

The expression

matches the pattern of the left side of the rule above. So according to the rule it must be equal to the right side of the rule:

which simplifies to

As usual, if you have trouble using the rules for exponents, work without them! In other words, rewrite your expressions without exponents and simplify without them.

becomes
2*2*2*2*2*2*2*5*5*5*5*5*5*5
This is all multiplication so we can use the Commutative Property of Multiplication to change the order as we please and we can use the Associative Property of Multiplication to rearrange the grouping as we please. So we can change the above to:
(2*5)*(2*5)*(2*5)*(2*5)*(2*5)*(2*5)*(2*5)
which simplifies to:
(10)*(10)*(10)*(10)*(10)*(10)*(10)
which can be rewritten as

RELATED QUESTIONS
Discuss why the expressions , and (8x) (4x) are not equivalent? (answered by Fombitz)

are the rational expressions a-b/b-a and b-a/a-b ( I cant put them in fraction... (answered by josgarithmetic,greenestamps)

explain why x+3=5 and x=2 are equivalent... (answered by ewatrrr)

are x<-5 and 2x>10 equivalent why or why not (answered by Fombitz)

Discuss why the expressions (8x / 4x), 8x � 4x and (8x)�(4x) are not equivalent? (answered by jsmallt9)

Are the equations x + 2 = 9 and 1 + x = 9 equivalent? Tell why or why... (answered by rfer)

Write two equivalent fractions & explain why they are equivalent. Thanks for... (answered by stanbon)

Are these functions inverse functions? Please explain why or why not in reference to the (answered by Fombitz)

1. A) Write the sentence (-x)2 � -x2 in words. In your own words... (answered by stanbon)