How do you simplify #(5x ^ { 3} ) ( 2x ) ^ { - 3}#?

2 Answers
Nov 27, 2017

#5/8#

Explanation:

Remember the PEMDAS. (Parenthesis, exponents, multiplication and division, addition and subtraction.)

You need to do #(2x)^-3# first, which is #1/ (2x)^3=>1/(8x^3)#
Now, multiply this by #5x^3#, which is #(5x^3)/(8x^3)#

Simplify the fraction. The numerator and the denominator shares #x^3# as its factor.

Therefore, our answer is #5/8#

Nov 27, 2017

Remember #u^(-a) = 1/u^a#. See explanation.

Explanation:

We will solve his both for the second term as written (#(2x)^(-3)#) , and for #2x^(-3)#. This second option has the exponent applied solely to the variable.

First, recall that by definition for any expression #u# and exponent #a#, #u^(-a)= 1/u^a#.

This means that..

#(2x)^(-3)=1/(2x)^3= 1/(8x^3)#

Multiplying by the First term then gives us...

#(5x^3)/(8x^3)=5/8#

If the second term was instead only applying the exponent to the variable, the 2 would remain in the numerator:

#2(x^(-3)) = 2/x^3#

In which case we instead have

#5x^3 × 2(x^(-3)) = 5x^3 * 2/x^3 = 2* = 10#