SOLUTION: explain the difference in the meaning of 4a and a to the 4th power.. and explain the difference in the meaning of -4b and b to the -4th power thank you

Algebra ->  Inequalities -> SOLUTION: explain the difference in the meaning of 4a and a to the 4th power.. and explain the difference in the meaning of -4b and b to the -4th power thank you      Log On


   

Question 175469: explain the difference in the meaning of 4a and a to the 4th power..
and
explain the difference in the meaning of -4b and b to the -4th power
thank you
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
explain the difference in the meaning of 4a and a to the 4th power..
4a is 4 times a. a to the 4th power (a^4) is a*a*a*a
As an example, if a is 5:
4a = 4*5 = 20
a^4 = 5*5*5*5 = 625
--------------
and
explain the difference in the meaning of -4b and b to the -4th power
-4b is -4*b
b%5E-4+=+1%2Fb%5E4
Negative exponents in the NUM are positive in the DEN.
Or you can look at it as:
%28%28b%5E-4%29%2F1%29%2A%28b%5E4%2Fb%5E4%29
=1%2Fb%5E4
As a numberical example, if b = 3:
-4b = -4*3 = -12
b^(-4) = 1/b^4 = 1/81
If b=0.6:
-4b = -2.4
b^(-4) = 1/0.1296 =~ 7.716
Note that a negative exponent does not mean it's a negative result.
Even when b = -7:
%28-7%29%5E-4+=+%2B1%2F2401
However, %28-7%29%5E3+=+-343, and
%28-3%29%5E-3+=+-1%2F27