Rewrite each expression as a repeated multiplication in three ways: using X, $\cdot$, and parentheses.

a. $3^4$ b. $5^6$ c. $\left( \frac{ 1 }{ 2 } \right)^3$

Solve the equation.

$$\sqrt { x + 6 } - \sqrt { 2 x - 4 } = 0$$

How much force would you need to cause a 20-kilogram object to accelerate in a straight line to 20 m/s^2?

Determine the inverse Laplace transform $f(t)$ of the function $F(s)= \frac{5}{s^{2}+s-6}$.

Make an order-of-magnitude estimate of the quantity. -The width of the smallest object that can be located using sound in the range of human hearing.

Find the solution of the equation if the replacement sets are x: {1, 3, 5, 7, 9} and y: {6, 8, 10, 12, 14}. 4y = 32

What is $\frac{3}{8}-\frac{1}{2}+\left(\frac{3}{4}\right)^{2}$?

Find $(-3 \cdot-4)-(-4 \cdot 2)$.

What is $4-12 \div 4 \cdot \frac{1}{2}-5^{2}$ ?

Use the information from Exercise 12 to find the area of your desktop that is not covered by the materials. Write a subtraction expression, and then give your answer as a single fraction in lowest terms.

Determine the missing value in each equation.

$$\begin{align*} &\text{a. } -3(-5) + 6 = \square &&\text{b. } 0.2(-14) - (-3) = \square \\ &\text{c. } \square + \frac{ 2 }{ 3 }(-9) = 7 &&\text{d. } \frac{ \square }{ 0.5 } - 6 = 0 \\ &\text{e. } \square - \frac{ 2 }{ 3 }(-6) = 10 &&\text{f. } \frac{ 10 }{ \square } - 3 = 2 \\ \end{align*}$$

Assume the area of your desktop is 1 square unit. Your math book covers $\frac{1}{4}$ of your desktop, your calculator covers $\frac{1}{16}$ of your desktop, and your scrap paper covers $\frac{1}{32}$ of your desktop. What total area is covered by these objects? Write an addition expression, and then give your answer as a single fraction in lowest terms.

How is the recursion process like drawing the Sierpinski triangle or like creating the Koch curve?

Write a word problem or draw a diagram that illustrates $\frac{3}{4}+\frac{1}{5}$ .