How do you simplify (5x3)(2x)−3?

2 Answers
Jarob R G.
Apr 6, 2018

(5x3)(2x)−3=58

Explanation:

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

In other words, a−n=1an.

So (5x3)(2x)−3=5x3(2x)3.

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

5x3(2x)3=5x38x3.

At this point, we notice that x3 is in the numerator and denominator, so it can be canceled. (Removed.)

5x38x3=58.

And 58 cannot be further simplified, so this is our final answer.

Note: It is also appropriate to mention that x≠0, since if x=0 then 5x38x3=00 and one cannot divide by zero.

emikokamoto .
Apr 6, 2018

58

Explanation:

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

(5x3)(2x)−3=5x3(2x)3

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

5x323x3=5x38x3

The last step is to cancel out the x3 terms which gives us:

58
We can do this because any number divided by itself is 1 which means:

5x38x3=58⋅x3x3=58⋅1

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

(5x3)(2x)−3=(5x3)(2−3)(x−3)

Now when we simplify this equation we get:

5⋅x3⋅18⋅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⋅18⋅x3⋅x−3=58x3+(−3)=58x0=58

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