Question

u5d1: rational exponents
score: 13/28 answered: 15/28
question 7
1st: rewrite in fractional - exponent form,
\\(\sqrt{x}\bullet x\\)

Explanation:

Step1: Rewrite square root as exponent

Recall that $\sqrt{x} = x^{\frac{1}{2}}$. The expression is $\sqrt{x} \cdot x$, so substitute $\sqrt{x}$ with $x^{\frac{1}{2}}$: $x^{\frac{1}{2}} \cdot x$.

Step2: Apply exponent multiplication rule

When multiplying terms with the same base, add the exponents: $x^a \cdot x^b = x^{a + b}$. Here, $a=\frac{1}{2}$ and $b = 1$ (since $x = x^1$), so $x^{\frac{1}{2}+1}=x^{\frac{3}{2}}$.

Answer:

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