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

2 Answers
Jarob R G.
Apr 6, 2018

#(5x^3)(2x)^(-3) = 5 / 8#

Explanation:

When you see some term raised to a negative power, it's really shorthand for division.

In other words, #a^-n = 1 / (a^n)#.

So #(5x^3)(2x)^(-3) = (5x^3)/(2x)^3#.

Notice that the #2# in the denominator is inside the parentheses, so we must raise it to the third power.

#(5x^3) / (2x)^3 = (5x^3) / (8x^3)#.

At this point, we notice that #x^3# is in the numerator and denominator, so it can be canceled. (Removed.)

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

And #5/8# cannot be further simplified, so this is our final answer.

Note: It is also appropriate to mention that #x ne 0#, since if #x = 0# then #(5x^3) / (8x^3) = 0 / 0# and one cannot divide by zero.

emikokamoto .
Apr 6, 2018

#5/8#

Explanation:

First, let's rewrite this without the negative exponent. The negative means that the term is in the denominator:

#(5x^3)(2x)^-3=(5x^3)/((2x)^3)#

Now, let's distribute the power in the denominator:

#(5x^3)/(2^3x^3)=(5x^3)/(8x^3)#

The last step is to cancel out the #x^3# terms which gives us:

#5/8#
We can do this because any number divided by itself is 1 which means:

#(5x^3)/(8x^3)=5/8*x^3/x^3= 5/8*1#

We can also approach the original problem a different way.
After we distribute the #-3# exponent, we get the following:

#(5x^3)(2x)^-3=(5x^3)(2^-3)(x^-3)#

Now when we simplify this equation we get:

#5*x^3*1/8*x^-3#

After rearranging this expression we can then use the rules of exponents. When you multiply terms with the same base you add their exponents together:

#5*1/8*x^3*x^-3=5/8x^(3+(-3))=5/8x^0=5/8#

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