Question

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

Answer 1

`5\ x^6`

Explanation:

Given expression:

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

Rules of exponents to be used:

`a^(-b)=(1)/(a^b)` [Rule of negative exponent]

`a^b\ .\ a^c=a^(b+c)` [Product Rule]

Using the above rules to simplify the given expression.

⇒
`5x\ .(1)/((1)/(x^7))\ .\ x^(-2)` [By rule of negative exponent]

⇒
`5x\ .\ x^7\ .\ x^(-2)` [Simplifying fractions]

⇒
`5\ x^(1+7-2)` [By product rule]

⇒
`5\ x^6` (Answer)