Product of Powers
If you are multiplying powers with the same base, what do you do?
Keep the base and add their exponents!
When dividing powers with the same base, what do you do?
Keep the base and Subtract the exponents
If you encounter a power to a power with the same base, what do you do?
Keep the base and multiply the exponents
To find a power of a product, what do you do?
Find the power of each factor and then multiply
To find the power of a quotient, what do you do?
Find the power of the numerator and the power of the denominator, and divide.
True or False. According to the Product of Powers Property, 42 multiplied by 43 equals 46.
False.
42 x 43 = 42 + 3 = 45
True of False. According to the Quotient of Powers Property, 1334 divided by 1331 power is equal to 1333.
True.
1334 / 1331 = 1334-1 = 1333
True or False. According to the Power to a Power Property, (64)-8 is equal to 64.
False. (64)-8 = 64 x -8 = 6-32 or 1/632
True or False. According to the Power of Product Property, (3y)6 is equal to 3y6.
False. (3 y)6 = 36 + y6 OR 729y6
True or False. (5/3)4 = 625/81
True. (5/3)4 = (54)/(34) = 625/81
What is 1018 multiplied by 103 ?
1021
What is 3132 divided by 384?
3132 / 384 = 3132- 84 = 348
What is (t12)8?
(t12)8 = t 12 x 8 = t96
What is (2 x 3)2?
(2 x 3)2 = 22 x 32 = 4 x 9 = 36
What is (2/3)5?
(2/3)5 = (25 / 35 ) = 32/243
Give a general rule, using algebra, to describe the Product of Powers Property.
What is (-6)9 divided by (-6)7?
(-6)9 / (-6)7 = (-6)9-7 = (-6)2 = 36
What is (4-2)-2?
What is (4d)3 / 24 ?
(4d)3 / 24 = (43 x d3) / 24 = 64d3/16
What is (5d/4)3?
(5d/4)3 = (53 x d3)/(43) = 125d3/64
1222 multiplied by 12x is equal to 1283, what is x?
12 22 + x = 1283, x = 61
What is y8 divided by y9?
1 divided by y.
y8 / y9 = y8-9 = y-1 or 1/y
If (22)y is equal to 1/64, what is y?
y = -3
(22)y = 2 2 x -3 = 2-6 or 1/ 26 or 1/64
What is (3y2)2?
(3y2)2 = 32 x (y2)2 = 32 x y2 x 2 = 32y4 or 9y4
What is (1/5s8)-3?
(1/5s8)-3 = (1 divided by 5-3 x s8 x -3) = 53s24 or 125s24