How do you simplify (5x ^ { 3} ) ( 2x ) ^ { - 3}(5x3)(2x)−3?

2 Answers
Parabola
Nov 27, 2017

5/858

Explanation:

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

You need to do (2x)^-3(2x)−3 first, which is 1/ (2x)^3=>1/(8x^3)1(2x)3⇒18x3
Now, multiply this by 5x^35x3, which is (5x^3)/(8x^3)5x38x3

Simplify the fraction. The numerator and the denominator shares x^3x3 as its factor.

Therefore, our answer is 5/858

Psykolord1989 .
Nov 27, 2017

Remember u^(-a) = 1/u^au−a=1ua. See explanation.

Explanation:

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

First, recall that by definition for any expression uu and exponent aa, u^(-a)= 1/u^au−a=1ua.

This means that..

(2x)^(-3)=1/(2x)^3= 1/(8x^3)(2x)−3=1(2x)3=18x3

Multiplying by the First term then gives us...

(5x^3)/(8x^3)=5/85x38x3=58

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^32(x−3)=2x3

In which case we instead have

5x^3 × 2(x^(-3)) = 5x^3 * 2/x^3 = 2* = 105x3×2(x−3)=5x3⋅2x3=2⋅=10

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