Exponent Rules
Write in exponential form.
a*a*b*b*a*a*a
Answer: a5b2
a*a*b*b*a*a*a
a*a*a*a*a*b*b
a^5b^2
Is the following expression written in scientific notation? If not, explain why. 3.25 + 10-7
Answer: No. Scientific Notation is written as a product, not a sum.
Should be 3.25 X 10-7
Suppose there are 5 × 106 bacteria in every liter of water. How many bacteria are there in 12 liters of water? Write the answer in Scientific Notation.
Answer: 6.0 x 107 bacteria
(5 × 106 )(12)
(5 x 12) (106)
60 x 106
6.0 x 107
Is -28 the same answer as (-2)8? Explain.
Answer: No, parentheses make the difference.
-2^8 = -(2*2*2*2*2*2*2*2) = -(256) = -256
(-2)^8 = (-2)(-2)(-2)(-2)(-2)(-2)(-2)(-2)= 256
Simplify 52 * 5-4 . Write in exponential form.
Answer: 5-2
When you multiply exponents:
Keep common base.
Add exponents.
52 * 5-4
52+-4
5-2
The mass of Jupiter is approximately 1,900,000,000,000,000,000,000,000,000 kg. Write the mass of Jupiter in scientific notation.
Answer: 1.9 x 1027
The population of the United States is 2×108 and the population of the world is 7×109 . How many times larger is the population of the world than the U.S.?Write the answer in standard form.
Answer: The world's population is 35 times larger than the U.S. population.
(7 x 10^9)/(2 x 10^8)
(7/2)(10^9/10^8)
3.5 x 10^9-8
3.5 x 10
35
What is the missing exponent? Find ?
(3^4)^? = (3^8)(3)(3^11)
Answer: ? = 5
(3^4)^? = (3^8)(3)(3^11)
(3^4)^? = (3^(8+1+11))
(3^4)^? = 3^20
(3^4)^5 = 3^20
3^20 = 3^20
Write in exponential form.
(12x^5y^3)/(4x^2y)
Answer: 3x3y2
1) Divide coefficients.
2) List bases.
3) Subtract exponents with common bases.
(12x^5y^3)/(4x^2y)
(12/4)(x^5/x^2)(y^3/y)
3(x^(5-2))(y^(3-1))
3x^3y^2
The mass of a Monarch butterfly is about 9.5 x 10-3. Write this number in standard form.
Answer: .0095
Move the decimal 3 spaces to the left.
A factory that has 6 X 103 workers makes 2.4 X 105 products each day. What is the average amount of products made per worker? Write the answer in Scientific Notation.
Answer: The average number of products made per worker is 4 × 10.
(2.4 x 10^5)/(6 x 10^3)
(2.4/6)(10^(5-3))
0.4 x 10^2
4 x 10
A student solved the following problem
(2 x 104)(1.8 x106) and said the answer is 3.6 x 10-2 Are they correct? Explain.
Answer: No they are not correct. They subtracted the exponents instead of adding them.
(2 x 104)(1.8 x106)
(2 x 1.8)(104 x 106)
(3.6)(10(4+6))
3.6 x 1010
Simplify.
(3c^5)^3
Answer:
27c^15
1) List bases.
2) Multiply the exponent of each base to its raised power.
(3c^5)^3
(3^(1*3))(c^(5*3))
27c^15
The size of the Sahara Desert is about 3.629 x 106 square miles and the Arabian Desert is about 9 x 105 square miles. Which desert is larger? Explain how you know.
Answer: The Sahara Desert is bigger.
The exponent of the Sahara is larger than the Arabian.
You can also compare by writing both in standard form.
Sahara: 3,629,000 miles2
Arabian: 900,000 miles2
The volume of Lake Rason is approximately 2.56 x 105 km3 . Lake Rushton is 25 times the volume of Lake Rason. What is the volume of Lake Rushton?
Answer: The volume of Lake Rushton is approximately 6,400,000 km3
(2.56 x 105)(25)
(2.56 x 25)(105)
64 x 105
6.4 x 106
6,400,000
Write 325 X 102 in Scientific Notation.
Answer: 3.25 x 104
325 X 102
3.25 x 10(2+2) Since the coefficient got smaller, the exponent gets larger.
3.25 x 104
Simplify and write using positive exponents.
(-10x^6y^5)(-x^2y)(2x^-10y^-3)
Answer:
(-10x^6y^5)(-x^2y)(2x^-10y^-3)
(-10*-1*2)(x^6*x^2*x^-10)(y^5*y*y^-3)
(20)(x^(6+2+ -10))(y^(5+1+ -3))
20x^-2y^3
(20y^3)/x^2
he size of the four oceans, in square km, is shown below. List the oceans from smallest to largest.
Pacific Ocean: 1.7965 x 108
Arctic Ocean: 1.323 x 107
Atlantic Ocean: 1.061 x 108
Indian Ocean: 7.49 x 107
Answer: Arctic, Indian, Atlantic, Pacific
Arctic Ocean: 1.323 x 107 13,230,000
Indian Ocean: 7.49 x 107 74,900,000
Atlantic Ocean: 1.061 x 108 106,100,000
Pacific Ocean: 1.7965 x 108 179,650,000
A rectangle has a length of (3.25 x 106) and a width of 200,000 cm. Find the area of the rectangle.
Answer: (6.5 x 1011) units2
Area = length x width
Write numbers in the same form.
Area = (3.25 x 106)(2 x 105)
Area = (3.25 x 2)(106 x 105)
Area = 6.5 x 10(6+5)
Area = (6.5 x 1011) units2
Evaluate the expression (5x3 -7y2)2
when x=2 and y=-3
Answer: 529
(5x3 -7y2)2
(5(2)3 -7(-3)2)2
(5(8) -7(9))2
(40 - 63)2
(-23)2
529