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

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) (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
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and
explain the difference in the meaning of -4b and b to the -4th power
-4b is -4*b

Negative exponents in the NUM are positive in the DEN.
Or you can look at it as:

=
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:

However, , and

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