Question

Question 2
Use the laws of exponents to simplify the expression so that the base, x, appears once, and the exponent is positive.

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Answer 1

The laws of exponents state that when dividing two terms with the same base, we can subtract the exponents. Therefore, to simplify the expression x^3/x^5, we can do the following:

x^3/x^5 = x^3/x^5 * x^2/x^2 = x^3 * x^(-5) * x^2 = x^(3 + (-5) + 2) = x^0 = 1

The base, x, appears once and the exponent is positive, which is 0.

So, x^3/x^5 = 1/x^2

Answer 2

Answer:

$\dfrac{1}{x^2}$

Step-by-step explanation:

Given rational expression:

$\dfrac{x^3}{x^5}$

$\textsf{Apply the exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:$

$\implies x^{3-5}$

Simplify:

$\implies x^{-2}$

$\textsf{Apply the exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:$

$\implies \dfrac{1}{x^2}$