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Ede4ka [16]
3 years ago
9

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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The roots of the entire <em>polynomic</em> expression, that is, the product of p(x) = x^2 + 8x + 12 and q(x) = x^3 + 5x^2 - 6x, are <em>x₁ =</em> 0, <em>x₂ =</em> -2, <em>x₃ =</em> -3 and <em>x₄ =</em> -6.

<h3>How to solve a product of two polynomials </h3>

A value of <em>x</em> is said to be a root of the polynomial if and only if <em>r(x) =</em> 0. Let be <em>r(x) = p(x) · q(x)</em>, then we need to find the roots both for <em>p(x)</em> and <em>q(x)</em> by factoring each polynomial, the factoring is based on algebraic properties:

<em>r(x) =</em> (x + 6) · (x + 2) · x · (x² + 5 · x - 6)

<em>r(x) =</em> (x + 6) · (x + 2) · x · (x + 3) · (x + 2)

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To learn more on polynomials, we kindly invite to check this verified question: brainly.com/question/11536910

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