Problem: Multiply $(3.0 \times 10^5)$ and $(4.0 \times 10^3)$ and express the result in scientific notation.

Solution:

Answer: $1.2 \times 10^9$

Problem: Simplify and write in radical form: $(16x^8)^{3/4}$

Solution:

Answer: $8x^6$

Problem: Simplify by converting to rational exponents: $\sqrt{x} \cdot \sqrt[3]{x^2}$

Solution:

Answer: $x\sqrt[6]{x}$

Problem: Rationalize the denominator: $\frac{4}{2 + \sqrt{5}}$

Solution:

Answer: $4\sqrt{5} - 8$

Problem: Solve for $x$: $\sqrt{3x + 13} = x + 3$

Solution:

Answer: $x = 1$