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

Answer:

$5\ x^6$

Step-by-step explanation:

Given expression:

$5x\ .\ \frac{1}{x^{-7}}\ .\ x^{-2}$

Rules of exponents to be used:

$a^{-b}=\frac{1}{a^b}$  [Rule of negative exponent]

$a^b\ .\ a^c=a^{b+c}$  [Product Rule]

Using the above rules to simplify the given expression.

⇒ $5x\ .\frac{1}{\frac{1}{x^7}}\ .\ x^{-2}$  [By rule of negative exponent]

⇒ $5x\ .\ x^7\ .\ x^{-2}$      [Simplifying fractions]

⇒ $5\ x^{1+7-2}$              [By product rule]

⇒ $5\ x^6$ (Answer)