SOLUTION: How would I do these problems? (1/a)^-1 = a a^-1/a^0 = 1/a And is this problem true? (4 + 5)^-1 = 4^-1 + 5^-1 Please show all work. Thank you!!!

Algebra ->  Exponents -> SOLUTION: How would I do these problems? (1/a)^-1 = a a^-1/a^0 = 1/a And is this problem true? (4 + 5)^-1 = 4^-1 + 5^-1 Please show all work. Thank you!!!      Log On


   

Question 134402: How would I do these problems?
(1/a)^-1 = a
a^-1/a^0 = 1/a
And is this problem true?
(4 + 5)^-1 = 4^-1 + 5^-1
Please show all work. Thank you!!!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
How would I do these problems? Just follow the rules of exponents
:
%281%2Fa%29%5E-1+=+a
Inverting the fraction gets rid of the neg exponent, so you just have
%28a%2F1%29%5E1+=+a
A number with an exponent of 1 is the same as just the number
a%2F1+=+a
which is:
a = a; true
:
:
%28a%5E-1%29%2Fa%5E0+=+1%2Fa
Remember any number with ^0 exponent is equal to 1, so you have
a%5E-1+=+1%2Fa
Write the number's reciprocal to get rid of negative
1%2Fa+=+1%2Fa; true
:
And is this problem true?
%284+%2B+5%29%5E-1+=+4%5E-1+%2B+5%5E-1
Do the math inside the brackets
9%5E-1+=+4%5E-1+%2B+5%5E-1
write the reciprocal of the each term to get rid of the negative
1%2F9+=+1%2F4+%2B+1%2F5; obviously this is not true
:
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