cartoonlens4
Answered

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

Type your response in the box.

Question 2 Use the laws of exponents to simplify the expression so that the base x appears once and the exponent is positive Type your response in the box class=


Answer :

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

semsee45

Answer:

[tex]\dfrac{1}{x^2}[/tex]

Step-by-step explanation:

Given rational expression:

[tex]\dfrac{x^3}{x^5}[/tex]

[tex]\textsf{Apply the exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\implies x^{3-5}[/tex]

Simplify:

[tex]\implies x^{-2}[/tex]

[tex]\textsf{Apply the exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]

[tex]\implies \dfrac{1}{x^2}[/tex]

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