simplify each expression.
a. y14 (y2) = y16 (add exponents)
b
(-9y3)4 = 6561y12 (multiply exponents)
c. 41 + 40 = 4 + 1 = 5 (anything to the zero power is always one)
d.
-80x0 = -80(1) = -80
e (3x-3)2(7x4) = (9x-6)(7x4) = 63x-2 = 63/x2 (negative exponents move to the
other side of the fraction bar.)
f.
g.
h.
i.
(3x2y-3)(-5x-1y4)2 = (3x2y-3)(25x-2y8) = 75x0y5 = 75y5
 5x 2 y 4

6
 2 xy

 = (5x)/(2y2) (subtract exponents when dividing)

3-2 + 2-1 = 1/9 + ½ = 11/18
x6 (x-2) = (x4)(x4) = x8
x-4
find each product.
a. -3x2y(6x4y3 - 5x3y +4y) = -18x6y4 + 15x5y2 - 12x2y2
b.
(2x + 3)(5x – 4) = 10x2 - 8x + 15x - 12 = 10x2 + 7x - 12 (FOIL)
c.
(4t – 7)2 = (4t - 7)(4t - 7) = 16t2 - 28t - 28t + 49 = 16t2 - 56t +49
d.
(3a – 4b)(3a + 4b) = 9a2 - 16b2 (Difference of squares)
e.
(5y – 2)(y2 - 4y + 3) = 5y3 - 20y2 + 15y - 2y2 + 8y - 6 = 5y3 - 22y2 + 23y -6
divide.
12x4 – 16x3 + 8x = 12x4/4x - 16x3/4x + 8x/4x = 3x3 - 4x2 + 2
4x
3x3 + 5x2 – 5x + 8
3x - 1
Write 2.14 x 10-4 in decimal notation: .000214
Write 2,201,000 in scientific notation: 2.201 x 106
Simplify 4.2 x 105
8.4 x 10-3
= (4.2/8.4)(105/10-3) = .5 x 108 = 5 x 107
Simplify (3.4 x 10-4)(4.1 x 105) = (3.4)(4.1)(10-4)(105) = 13.94 x 101 = 139.4
Write a polynomial in descending powers of x that represents the area of
the rectangular garden below: (x + 5)(x + 3) = x2 + 3x + 5x + 15 = x2 + 8x + 15
x
x
3
5
The mass of a proton is approximately 1.7 x 10-24 gram. Find the mass of 5
billion protons. Express your answer in scientific notation
(5 x 109)(1.7 x 10-24) = 8.5 x 10-15 grams
What is the volume of a box whose length is 12 – 2x, width is 7 – 2x and
height is x?
x(12 - 2x)(7 - 2x) = x(84 - 24x - 14x + 4x2) = x(84 - 38x + 4x2) = 4x3 - 38x2 + 84x
A bacterium measures 0.00000000896 centimeters. Rewrite the number in
scientific notation.
8.96 x 10-9
A rectangle with width 3x – 4 has an area of 6x2 + 7x – 20. Find the
binomial that represents its length.
(2x + 5) because (3x - 4)(2x + 5) = 6x2 + 15x - 8x - 20 = 6x2 + 7x – 20