Explain Your Thinking
How can you write and evaluate numbers with exponents?
Write the number that is multiplied repeatedly as the base, and write the number of times the number is multiplied as the exponent. Use repeated multiplication to evaluate the power.
Write in exponential form and solve
9 x 9 x 9 x 9
9^4 = 6561
Expand and solve. Round to the nearest hundreth.
1.2^9
1.2 x 1.2 x 1.2 x 1.2 x 1.2 x 1.2 x 1.2 x 1.2 x 1.2 = 5.16
A marine biologist studies the population of seals in a research area. How many seals are in the research area is the population is 3.27 x 10^2?
327 seals
How many times is 4 used as a factor in the expression 4^5? Write the numerical expression in expanded form and solve.
4 x 4 x 4 x 4 x 4 = 1024
Write in exponential form and solve
1/6 x 1/6 x 1/6
(1/6)^3 = 1/216
Solve 7^0
1
An astronomer measures the distance to a nearby asteroid. How far away is the asteroid if the distance is
4.5 × 10³ kilometers?
4,500 km
What is a power that has the same value as 1^8?
1^5, anything^0
0.6 x 0.6
0.6^2 = 0.36
Expand and solve
8^3
8 x 8 x 8 = 512
A chemist analyzes a sample of ocean water. How many salt particles are in the sample if the number is 6.02 × 10⁴ particles?
60,200 particles
Does 2.5 x 10^0 equal 0, 1, 2.5 or 25? Explain
2.5; 10^0 is 1 and 1 x 2.5 = 2.5
2/5 x 2/5 x 2/5 x 2/5 x 2/5
(2/5)^5 = 32/3125
Expand and solve
(1/5)^4
1/5 x 1/5 x 1/5 x 1/5 = 1/625
A rainforest researcher counts the number of ants living in a square meter of forest floor. How many ants are there if the population is 8.9 × 10⁵ ants?
890,000 ants
How would you write (1/2)^3 as repeated multiplication? What is the answer?
1/2 x 1/2 x 1/2 = 1/8
2/3 x 2/3 x 2/3
(2/3)^3 = 8/27
Solve 6.2 x 10^3
6200
A physicist studies the speed of an experimental robot. How fast is the robot moving if its speed is 2.15 × 10² meters per second?
215 m/s