Simplify the Expression: x⁶/x² Using Exponent Rules

To solve this problem, we'll follow these steps:

• Step 1: Identify the common base in both the numerator and the denominator.

• Step 2: Apply the Power of a Quotient Rule for Exponents.

• Step 3: Simplify the expression by subtracting the exponents.

Now, let's work through each step:
Step 1: Notice that both the numerator $x^6$ and the denominator $x^2$ share the same base, $x$.
Step 2: The Power of a Quotient Rule states that $\frac{a^m}{a^n} = a^{m-n}$. We apply this rule to our expression, obtaining $x^{6-2}$.
Step 3: Simplifying $6 - 2$, we find that the expression simplifies to $x^4$.

Therefore, the simplified form of the expression $\frac{x^6}{x^2}$ is $x^4$.

Considering the given answer choices:

• Choice 1: $x^{6+2}$ is incorrect because it involves adding the exponents, which does not follow the rules for division of powers.

• Choice 2: $x^{6-2}$ is the correct as the setup simplification, and can be fully simplified to yield $x^4$ for clarity.

• Choice 3: $x^{6\times2}$ is incorrect because it multiplies the exponents, which is not applicable in division.

• Choice 4: $x^{\frac{6}{2}}$ is not directly applicable as it assumes a different interpretation not aligning with subtraction of exponents for division.

The correct choice is represented by choice 2, $x^{6-2}$.