what is the following product? assume $ygeq0$.\n$sqrt{y^{3}}cdotsqrt{y^{3}}$\n$y^{3}$\n$2y^{3}$\n$y^{6}$\n$2y…
what is the following product? assume $ygeq0$.\n$sqrt{y^{3}}cdotsqrt{y^{3}}$\n$y^{3}$\n$2y^{3}$\n$y^{6}$\n$2y^{6}$
Answer
Answer:
A. $y^{3}$
Explanation:
Step1: Use square - root multiplication rule
$\sqrt{a}\cdot\sqrt{a}=a$ and $\sqrt{y^{3}}\cdot\sqrt{y^{3}}=\sqrt{y^{3}\cdot y^{3}}$
Step2: Apply exponent rule for multiplication
$y^{3}\cdot y^{3}=y^{3 + 3}=y^{6}$ (since $a^{m}\cdot a^{n}=a^{m + n}$), so $\sqrt{y^{3}\cdot y^{3}}=\sqrt{y^{6}}$
Step3: Simplify the square - root
$\sqrt{y^{6}}=y^{3}$ (because $\sqrt{a^{n}}=a^{\frac{n}{2}}$ and when $n = 6$, $\frac{6}{2}=3$)