Question

the image shows a mathematical expression oriented sideways. when rotated 90 degrees clockwise, it reads:

\\ \frac{x^2}{x^{1/2}} \\

simplify the expression.

Explanation:

⚡ Using what you learned: properties of exponents

Step 1: Identify the expression

The image shows a division of two exponential terms containing the variable \( x \). Note that the image is rotated \( 90^\circ \) counterclockwise. When rotated to its correct orientation, the expression is:

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

Step 2: Apply the quotient rule of exponents

To divide powers with the same base, subtract the exponent in the denominator from the exponent in the numerator:

$$ x^{2 - \frac{1}{2}} $$

Step 3: Simplify the exponent

Subtract the fractions:

$$ 2 - \frac{1}{2} = \frac{4}{2} - \frac{1}{2} = \frac{3}{2} $$

Thus, the simplified expression is:

$$ x^{\frac{3}{2}} $$

Answer:

$$ x^{\frac{3}{2}} \text{ (or } \sqrt{x^3} \text{)} $$