NAEP Grade 12 Number Properties and Operations. Practice it free.

Multiply coefficients and add exponents: $5 \cdot 4 = 20$ and $-3+(-2)=-5$, giving $20 \times 10^{-5}$. Rewrite $20=2 \times 10^{1}$, so $2 \times 10^{1} \times 10^{-5}=2 \times 10^{-4}\textsf{.}$

$\sqrt{28}=2\sqrt{7}$, $\sqrt{63}=3\sqrt{7}$, and $\sqrt{7}=\sqrt{7}$. Adding gives $2\sqrt{7}+3\sqrt{7}+\sqrt{7}=6\sqrt{7}$.

A square root divides each exponent by $\Large 2$: $\Large x^{\tfrac{10}{2}} y^{\tfrac{8}{2}} = x^5 y^4$.

The product is $12 \cdot 64 = 768$. Factor $768 = 256 \cdot 3$, where $256$ is the largest perfect-square factor. So $\sqrt{768} = \sqrt{256 \cdot 3} = 16\sqrt{3}$, and $3$ is square-free.

$16^{1/2} = \sqrt{16} = 4$.

$9800 = 70^2 \cdot 2$, so $\sqrt{9800} = 70\sqrt{2}$.

Multiply by conversion factors so the old units cancel: $3\,\text{gal} \times \dfrac{4\,\text{qt}}{1\,\text{gal}} \times \dfrac{4\,\text{cups}}{1\,\text{qt}} = 48\,\text{cups}$.

Divide coefficients and subtract exponents: $6.3 \div 2.1 = 3$ and $-4-(-9)=5$. So the quotient is $3 \times 10^{5}\textsf{.}$