Sketch models to represent each of the following algebraic expressions. The variables x and y are not equal.

\displaystyle y^2

Sketch models to represent each of the following algebraic expressions. The variables x and y are not equal.

\displaystyle y^3

Sketch models to represent each of the following algebraic expressions. The variables x and y are not equal.

\displaystyle 2x

Sketch models to represent each of the following algebraic expressions. The variables x and y are not equal.

\displaystyle (2x)^2

Rob is finishing a floor with square tiles. Each tile has an area of 412 cm^2. Estimate the length of the side of each tile.

Why do you get the same result for each of the following expressions? Show your work using Exponent Laws.

(a) \displaystyle \frac{5^7}{5^4}

(b) \displaystyle \frac{5^6}{5^3}

(c) \displaystyle\frac{(5^4)(5^5)}{5^6}

(d) \displaystyle\frac{(5^4)(5)}{(5)(5)}

Simplify, and then evaluate for x = -2 and y = 3

\displaystyle \frac{(x^3)(x^4)}{x^6}

Simplify, and then evaluate for x = -2 and y = 3

\displaystyle \frac{(y^6)(x^4)}{(x^2)(y^4)}

Simplify, and then evaluate for x = -2 and y = 3

\displaystyle \frac{-32x^6}{16x^3}

If you know that the product of two numbers is 9^6 and quotient is 9^2, which of the following could be the two numbers?

About how long does it take for light to travel from one end of our galaxy to the other?

• It is about 9.5 \times 10^6 km from one end of our galaxy to the other.
• Light travels at about 1.1 \times 10^9 km/h.

Simplify.

\displaystyle (a^3)^2

Simplify.

\displaystyle (4x^3)^4

Simplify.

\displaystyle \frac{(2^3y^4)^3}{(2^4y^3)^2}

Which of the following is equal to 0?

• a)(10^3)^5 -(10^5)^3
• b) (9^2)^2-(3^4)^2

Express each of the following as a power with a prime base.

8^3

Express each of the following as a power with a prime base.

25^4

Express each of the following as a power with a prime base.

9^3

The length of the side of a cube is 5^3. Express its surface area (SA) and volume (V) using powers and simplify each expression.

Simplify.

\displaystyle 5y -4y

Simplify.

\displaystyle 3xy^2 + 3xy^2

Simplify.

\displaystyle 2x^2 - 5x + 5x^2 -x

Simplify.

\displaystyle y^2 + 5xy + y^2 - xy

Simplify.

\displaystyle \frac{4}{5}a - \frac{1}{5}a

Simplify.

\displaystyle 2\frac{1}{2}a + \frac{2}{3}b + \frac{1}{2}a-\frac{1}{3}b

Simplify.

\displaystyle -1.75m + 2.7 -2.25m + 2.3

Mindy and Kimberly have a picture framing business. Mindy cuts the wooden frames. She charges \$ 25 for each one plus \$10/h for her labour. Kimberly cuts the picture mats and assemblies the product. She assembles $ 8 for each mat plus \$ 9/h for her labour.

(a) Represent Mindy's bill as a polynomial.

(b) Represent Kimberly's bit las a polynomial.

(c) Write a new polynomial that represents their total charge to dream a picture. Assume that they both work h hours on the frame.

(d) Calculate the cost for a frame if they both work 5 h on it.

Expand. check one of your answer using a different tool or strategy.

3(y - 2)

Expand. check one of your answer using a different tool or strategy.

x(2x+ 4)

Expand. check one of your answer using a different tool or strategy.

5m(3m^3 + 2n)

Expand. check one of your answer using a different tool or strategy.

-3x(x^2 -x)

Expand. check one of your answer using a different tool or strategy.

2y^3(y^3 + 3y^2 - y)

Expand. check one of your answer using a different tool or strategy.

-a^2(2a -5a^2+4a^3)

Expand.

\displaystyle \frac{1}{3}(3x +12)

Expand.

\displaystyle \frac{2}{5}(\frac{5}{8}a +10b)

Expand.

-1.5m(2.8m + 2.2)

Rick runs a pet store and is building rectangular pens for the animals. The length of the pens is always 20 cm longer than the width.

(a) One way of determining the perimeter is to use P = 2(l + w). Use this formula to create an expression for the perimeter in terms of x.

(b) Simplify your formula in part (a).

Rick runs a pet store and is building rectangular pens for the animals. The length of the pens is always 20 cm longer than the width.

• Find the perimeter of a pen with a width of 45 cm.

Expand and simplify. Check one of your answers using a different tool or strategy.

2(x - 3) + 3(x + 2)

Expand and simplify. Check one of your answers using a different tool or strategy.

3(y^2 + y-2)-(y^2+2y+4)

Expand and simplify. Check one of your answers using a different tool or strategy.

2x(3x - 2) + x^2 + 2(x^2+3)

Expand and simplify. Check one of your answers using a different tool or strategy.

3x(4x^2-5x) + x^3 -x^2

Ms. Smith needs fabric pieces for an art project for her students. The pieces will be cut to two rectangular sizes, as shown.

Determine a simplified expression for the area of fabric needed if 14 students choose the larger size and 12 choose the smaller size.

Ms. Smith needs fabric pieces for an art project for her students. The pieces will be cut to two rectangular sizes, as shown.

The class decides that the width of each piece of fabric will be 20 cm. Use your answer from part a) to determine how much material will be needed.

Expand and simplify.

\displaystyle \frac{1}{4}(8x - 12) -\frac{1}{2}(6 - 14x)

Expand and simplify.

\displaystyle \frac{5}{6}(6x - 18y) +\frac{2}{3}(21x - 6y)

Expand and simplify.

\displaystyle \frac{5}{6}(6x - 18y) +\frac{2}{3}(21x - 6y)

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

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

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

Determine the combined value of the cards in 6 years.