Q: Which of the following correctly applies the negative exponent rule to $$\left(3.2 \times 10^4$\$$right)^{-2}$$?

$$3.2^{-2}$$ \times $$10^{-8}$$

Question 1

Simplify the following expression using a calculator. Use $$3.14$$ for $$\pi$$.

$$\displaystyle \frac{\left(7.74 	imes 10$$^{-6}$$\$$right)^2$$ \left(1.1 	imes 10^8$\$$right)^{-5}$$}{\pi \left(4.6 	imes 10$$^{-2}$$\$$right)^3$$}$$

Which of the following is closest to the correct answer?

Accepted Answer

$$3.1 	imes 10$$^{-28}$$

Question 2

Which property of exponents is used to simplify $$\left(a^m\right)^n$$?

Accepted Answer

Power of a Power Property: $$\left(a^m\right)^n = a$$^{mn}$$

Question 3

If $$x = 2.5 	imes 10^3$ and y = 4$$ 	imes $$10^{-2}$$, what is $$\frac{x}{y} in $$scientific notation?

Accepted Answer

$$6.25 	imes 10^5$

Question 4

Which of the following correctly applies the negative exponent rule to $$\left(3.2 	imes 10^4$\$$right)^{-2}$$?

Accepted Answer

$$3.2^{-2}$$ 	imes $$10^{-8}$$

Question 5

A scientist measures a quantity as $$5.6 	imes 10$$^{-7}$$ meters. If she squares this value, what is the result in scientific notation?

Accepted Answer

$$3.136 	imes 10$$^{-14}$$

Question 6

Which of the following is equivalent to $$\frac{a^m}{a^n}$$?

Accepted Answer

$$a^{m-n}$$

Question 7

Evaluate $$\left(2.5 	imes 10^3$\$$right)^2$$ and express your answer in scientific notation.

Accepted Answer

$$6.25 	imes 10^6$

Question 8

Which of the following is the correct simplification of $$\frac{5.0 	imes 10$$^{-3}$$}{2.0 	imes 10^4$}$$?

Accepted Answer

$$2.5 	imes 10$$^{-7}$$

Question 9

A medical test result is $$4.6 	imes 10$$^{-2}$$ grams. If the result is cubed, what is the value in scientific notation?

Accepted Answer

$$9.73 	imes 10$$^{-5}$$

Question 10

Which of the following is the correct value for $$\pi as $$used in the provided study materials?

Accepted Answer

$$3.14$$

Question 11

If $$a = 7.74 	imes 10$$^{-6}$$, what is a^2$ in scientific notation?

Accepted Answer

$$5.99 	imes 10$$^{-11}$$

Question 12

Which of the following is the correct simplification of $$\left(1.1 	imes 10^8$\$$right)^{-5}$$?

Accepted Answer

$$1.61 	imes 10$$^{-40}$$

Question 13

Which exponent rule is used to simplify $$a^m \cdot a^n$$?

Accepted Answer

Product of Powers Property: $$a^m \cdot a^n = a$$^{m+n}$$

Question 14

A chemical reaction produces $$2.0 	imes 10$$^{-3}$$ moles of a substance. If the amount is divided by 4.0$$ 	imes $$10^2$$, what is the result in scientific notation?

Accepted Answer

$$5.0 	imes 10$$^{-6}$$

Simplifying Expressions with Exponents and Scientific Notation

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