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

Mathematics

1 answer:

loris [4]3 years ago

3 0

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)

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