Q: Which law of exponents allows you to simplify $$10^a \times 10^b$$?

$$10^a \times 10^b = 10$$^{a+b}$$

Q: Which of the following is NOT a law of exponents?

$$10^a \times 10^b = 10$$^{ab}$$

Question 1

Which of the following correctly expresses the meaning of $$\log_b(a) = k$$?

Accepted Answer

$$b^k = a$$

Question 2

Using the laws of exponents, simplify $$10^2$$ 	imes $$10^3.$$

Accepted Answer

$$10^5$$

Question 3

What is the value of $$(10^2)^3$?

Accepted Answer

$$10^6$$

Question 4

Which law of exponents allows you to simplify $$10^a 	imes 10^b$$?

Accepted Answer

$$10^a 	imes 10^b = 10$$^{a+b}$$

Question 5

If $$10^3$$ 	imes $$10^4 is $$computed, what is the result?

Accepted Answer

$$10^7$$

Question 6

Simplify $$\frac{10^3$}{10^4$}$$ using the laws of exponents.

Accepted Answer

$$10^{-1}$$

Question 7

Evaluate $$(10^3)^4$.

Accepted Answer

$$10^{12}$$

Question 8

Which of the following is the correct simplification for $$(10^2$$ 	imes $$10^3)^4$?

Accepted Answer

$$10^{20}$$

Question 9

Using the laws of exponents, simplify $$\frac{10^2$ 	imes 10^6$}{10^2$ 	imes 10^3$}.$$

Accepted Answer

$$10^3$$

Question 10

Evaluate $$\left(\frac{10^2$}{10^5$}\$$right)^{-2}$$.

Accepted Answer

$$10^6$$

Question 11

What is the value of $$(10^{0.5})^2$?

Accepted Answer

$$10^1$$

Question 12

If you compute $$(10^{0.1}$$)^{10}$, what do you get?

Accepted Answer

$$10^1$$

Question 13

Which of the following is the correct value for $$10^{0.27}$$?

Accepted Answer

Approximately $$1.86$$

Question 14

The distance to the nearest star (excluding our Sun) is approximately $$10^{17}$$ meters. Which law of exponents would you use to express this distance in terms of light years, given that one light year is $$10^{16}$$ meters?

Accepted Answer

$$\frac{10$$^{17}$$}{10$$^{16}$$} = 10^1$

Question 15

Which of the following is NOT a law of exponents?

Accepted Answer

$$10^a 	imes 10^b = 10$$^{ab}$$

Question 16

If the size of the universe is $$10^{26}$$ meters and the size of the solar system is $$10^{14}$$ meters, how many times larger is the universe than the solar system?

Accepted Answer

$$10^{12}$$ times larger

Question 17

Which of the following is the correct simplification for $$10^{-a}$$?

Accepted Answer

$$\frac{1}{10^a}$$

Question 18

If $$10^0 = 1$, what is the value of 10^0$ 	imes 10^5$?

Accepted Answer

$$10^5$$

Question 19

A scientist measures a distance as $$10^9$$ meters. If this is the distance to the moon, how many times farther is the size of the universe ($$10^{26}$$ meters) compared to the moon?

Accepted Answer

$$10^{17}$$ times farther

Question 20

Which of the following best describes the relationship between logarithms and exponents?

Accepted Answer

Logarithms are the inverse operation of exponents.

Lecture 9 - Intro: Logarithms and Laws of Exponents: Foundations for Calculus

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