Exponents
Question 6.
Compare expression to 6^6.
(6^−1⋅6^4)^2
Equal to 6^6
Question 10.
A bee hummingbird has a mass of 0.0023 kilogram. What is the mass of a bee hummingbird written in scientific notation?
2.3 X 10^-3
Question 8.
What are possible values for a and b in the equation 4^a/4^b=4^−1
Vary answers.
a=3 b=4
Change 0.0000035 from standard form to scientific notation.
3.5 X 10^6
Question 6.
Compare expression to 6^6.
6^6/(6^2)^2
Less than 6^6
Naomi says that 9.8×10^5 is greater than 3.2×10^6. Is Naomi correct? Explain your reasoning.
No, Naomi is not correct because the exponent with the base of 10 is less than 3.2 X 10^6. 6 is greater than 5.
What must be true about the values of a and b?
The value of b must be 1 more than the value of a.
Question 14.
Explain why in this situation, using millimeters per year for the rate is more appropriate to use than meters per day.
The rate can now be written without using scientific notation or a large number of zero digits.
Questions 5.
Write an expression with a single exponent that is equivalent to 8^−4 ⋅(8^2)^4.
8^4
Which expression is equivalent to
(1.2×10^−4)+(2.4×10^−3)?
2.52 X 10^-3
Which property of exponents must be applied when simplifying the expression (2^14)/(2^−3)?
Quotient of Powers Property
Question 14.
Mount Everest is growing at a rate of about 1.1×10^−5 meters per day.
Express this rate using millimeters per year and round to the nearest whole number.
4.0mm
Questions 6.
Compare expression to 6^6.
(6^2/6^0)^4
Greater than 6^6.
Question 9.
The diameter of Earth is about 1×10^4 kilometers, and the diameter of a basketball is about 2×10^−4 kilometer. About how many times as great is the diameter of Earth as the diameter of a basketball?
c. 50,000,000 times as great.
Amber uses her calculator to find how much farther Pluto is from the sun compared to Venus. The calculator shows the difference as 5.892E9 What is the difference in kilometers written in scientific notation and standard form?
5.892 X 10^9
5,892,000,000km
Question 13.
What is the difference between 8.5×10^−4 and 2.8×10^−4, written in standard form?
.00057
Question 7
Select all the expressions equivalent to (9^3⋅9^5)/9^2
b. 3^12
c. 9^6
f. 27^4
Question 12.
Which expression is equivalent to [(8×10^3)+(4×10^3)]/3×10^−2?
4 X 10^5
Evaluate the expression
(2×10^−3)+(4×10^2)×(1×10^−5).
6 X 10^-3
Question 15.
An elephant has a mass of 4500 kilograms. How many mice, with a mass of 2×10^−2 kilogram each, would it take to equal the mass of the elephant? Write your answer in standard form.
225,000