How do you rewrite #1/(4b^3)# using negative exponents?

1 Answer
Jan 2, 2016

Answer:

#4^(-1)b^(-3)#

Explanation:

Suppose we had #1/x#. This would have a particular value. If you turned it upside down to give #x/1# you have changed in inherent value so you need to apply a conversion.

The conversion used in this example is #x^(-1)#.

Although this looks deferent it has the same value as #1/x#

#color(green)("Note that "x" is the same as "x^1)#
so #1/x^1 = x^(-1)#

What if we had #1/(x^3)# then we would write: #x^(-3)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Dealing with your question using the same logic.

Given : #1/(4b^3)#

#color(blue)("Assumption")#

#color(brown)(underline("Everything")" is meant to have negative exponents")#

Initially write it as: #1/4 xx1/b^3#

Now write as: #1/4 xx b^(-3)/1 = (1 xx b^(-3))/(4 xx 1)#

So now we have: #b^(-3)/4#

You could take this further by starting to 'play' with #1/4#

One potential format would be: #4^(-1)b^(-3)#

Another: another way of writing 4 is #2^2#

So we could write: #color(white)(..)4^(-1)b^(-3)color(white)(.)" as "color(white)(.)2^(-2)b^(-3)#

Which is equally true!