Question 175469
 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
{{{b^-4 = 1/b^4}}}
Negative exponents in the NUM are positive in the DEN.
Or you can look at it as:
{{{((b^-4)/1)*(b^4/b^4)}}}
={{{1/b^4}}}
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:
{{{(-7)^-4 = +1/2401}}}
However, {{{(-7)^3 = -343}}}, and
{{{(-3)^-3 = -1/27}}}