Describe the relationship between the power-of-a-power principle and the other exponent principles you know.

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Two polynomials are added and the sum is $3 x^2-y+4$. For each statement, state whether it is always true, sometimes true, or never true. Explain or provide a counter-example to justify your answer.

a) Both are monomials.

b) Both include a $y$-term.

c) If there is an $x$-term in one polynomial then there must be an $x$-term in the other.

d) Both are binomials.

Knowing that $2^3$ is 8 and $3^2$ is 9 , how do you know that $2^{30}<3^{20}$ ?

Simplify.

a) $(2 x+3 y)+(5 x-4 y)+(2 x-y)$

b) $-(4 a b-3 a)-(6 a b-4 a)+(2 a b+6 a)$

c) $\left(3 x y+5 y^2\right)-\left(3 x y+5 y^2\right)+\left(3 x y+5 y^2\right)$

Write each power in simplified form. a) $4^5$ as a power of 2

b) $9^6$ as a power of 3

c) $27^4$ as a power of 3

d) $(-125)^7$ as a power of $(-5)

how is information to make proteins passed on through generations

Which DNA bases pair with each other? How many hydrogen bonds are shared by each pair?

What might be in the ethanol/aqueous interface? How could you eliminate this?

Mickey has a baseball card collection. He is wondering about the future value of his rookie and big star cards.

$$\begin{array}{|l|c|c|c|} \hline \text { Card Type } & \begin{array}{c} \text { Number } \\ \text { of Cards } \end{array} & \begin{array}{c} \text { Value } \\ \text { Today } \end{array} & \begin{array}{c} \text { Increase in } \\ \text { Value per Year } \end{array} \\ \hline \text { Rookie cards } & 22 & \$ 15 & \$ 3 \\ \hline \text { Big star cards } & 18 & \$ 12 & \$ 2 \\ \hline \end{array}$$

a) Write an expression that represents the combined value of these cards in $y$ years.

b) Use your answer from part a) to determine the combined value of the cards in 6 years.

Simplify.

a) $2 x+3 y+4 z-4 x+3 y-z$

b) $-4 a b c-3 a b-6 a b c-4 a b$

c) $3 x y+5 y z-2 x y z+6 x y-x y z$

Simplify.

a) $\frac{2^5}{2^2}$

b) $\frac{y^6}{y^3}$

Draw a diagram or make a model to represent each of the following:

a) $(3 y)^2$

b) $3 y$

c) $y^3$

Expand.

a) $2 a^3\left(4 a^2-a\right)$

b) $-2\left(y^2-y-1\right)$