Question

Simplify 5 x times the fraction 1 over x to the power of negative 7 times x to the power of negative 2. 5x 5x−6 5 5x6

Answer 1

• 
  `5x^6`

Step-by-step explanation:

The expression that you want to simplify is:

• 
  `5x* (1)/(x^(-7))* x^{-2`

This is the simplification step-by-step:

1. Mulitply the expressions on the numerator among them and the expressions on the denominator among them:

`5x* (1)/(x^(-7))* x^(-2)=(5x\cdot x^(-2))/(x^(-7))`

2. For equal bases that are multiplying, add the exponents:

`(5x\cdot x^(-2))/(x^(-7))=(5x^(1-2))/(x^(-7))=(5x^(-1))/(x^(-7))`

3. Pass the power on the denominator to the numerator by changing its sign (negative exponents become positive when inverted)

`(5x^(-1))/(x^(-7))=5x^(-1)x^(7)`

4. Simplify adding the exponents with the same base:

`5x^(-1)x^(7)=5x^(-1+7)=5x^6`

And that is the final expression in its most simple form.