Name: ___________________________ Date:__________________Pd._____ Exponent Rules Review Worksheet Product Rule: When multiplying monomials that have the same base, add the exponents. xm × xn = xm+ n Example 1: x × x3 × x 4 = x1+ 3+ 4 = x8 2 3 4 2 3 4 5 5 Example 2: 2 x y − 3x y = 2 ×( − 3) × x × x × y × y = − 6 x y
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)(
)
Power Rule: When raising monomials to powers, multiply the exponents.
(x )
m n
= x m×n
Example 3: (x2y3)4 = x2 • 4 y3 • 4 = x8y12 Example 4: (2x3yz 2)3 = 23 x3 • 3 y3 z2 • 3 = 8x9y3z6 Quotient Rule: When dividing monomials that have the same base, subtract the exponents. xm = xm− n xn x3 56 Example 5: − 2 = x 3− ( − 2) = x 5 Example 6: 2 = 56 − 2 = 54 x 5 3 5 3 5 36m n 36 m n Example 7: = × × 4 = − 4m 2 n 4 − 9mn −9 m n Simplify each of the following. Copy the problem. Work on your own paper. 1) a × a 2 × a 3
Simplify. Your answer should contain only positive exponents. (Hint: Use 1)
n
-2
0
-3
2)
(2n - 1 ) - 4
2
3)
× 2n
n × 2n
-3
×n
(n 2 ) 2
4)
p p
laws of exponents)
4
(2 p 3 ) 3
( ) x × 2x 2x
-1
-4
Find the discriminant of each quadratic equation then state the number and type of solutions. (Hint: The discriminant is the b^2 -4ac part of the quadratic formula.) 5) - 2b 2 - 8b - 8 = 0
Use the information provided to write the intercept form equation of each parabola. (Hint: Use Greatest Common Factor and then factor. EX: 27) y = - 8 x 2 - 16 x + 280
28) y = -
29) y = 2 x 2 - 2 x - 12
1 2 13 x + x - 21 2 2
30) y = x 2 + 11 x + 24
Identify the vertex, axis of symmetry, direction of opening, min/max value, and x-intercepts of each. Then sketch the graph. 31) y = x 2 + 10 x + 24
Solve each equation with the quadratic formula. Leave answers in simplified radical form. (Hint:You need to make a quadratic expression equal to zero before using the quadratic formula .) 41) 6n 2 + 4n = 10
42) v 2 - 19 = 10v
43) 3 p 2 + 5 p = 2
44) 4 p 2 = - 3 p + 7
Sketch the graph of each lin ear equation. (Hint:You need to get the Y value by itself to determine the slope and the Y-Intercept.) 45) 5 x - 4 y = 20