Question 1

Which of the following expressions is always positive for any real values of $$x$$ and $$y$$?

Accepted Answer

$$(x^3y^4$)^2$$

Question 2

Given $$\dfrac{2^4$}{2^2$}$$, which of the following is the correct simplification?

Accepted Answer

$$2^2$$

Question 3

If you have $$\dfrac{(x^3$y^4)^2$}{(x^3$y^4)^2$}$$, what is the result?

Accepted Answer

$$1$$

Question 4

When simplifying $$\dfrac{(x^3$y^4)^2$}{(x^3$y^4)^2$}$$, which mathematical property is being used?

Accepted Answer

Any nonzero number divided by itself is 1

Question 5

What is the value of $$\dfrac{2$$^{12}$$}{2^8$}$$?

Accepted Answer

$$2^4$$

Question 6

If you move the decimal point 5 places to the left in the number 475000, what is the result in scientific notation?

Accepted Answer

$$4.75 	imes 10^5$

Question 7

Which of the following numbers has a negative exponent when written in scientific notation?

Accepted Answer

$$0.0000072$$

Question 8

What is $$0.0000072$$ expressed in scientific notation?

Accepted Answer

$$7.2 	imes 10$$^{-6}$$

Question 9

If you move the decimal point 2 places to the left in the number 123, what is the result in scientific notation?

Accepted Answer

$$1.23 	imes 10^2$

Question 10

Which of the following is the correct way to multiply two numbers in scientific notation: $$4.75 	imes 10^5$ and 2$$ 	imes $$10^3$$?

Accepted Answer

$$9.5 	imes 10^8$

Question 11

If $$x = 2$$ and $$y = 3$$, what is the value of $$(x^3y^4$)^2$$?

Accepted Answer

$$20736$$

Question 12

Which of the following is true about the sign of a real expression raised to an even power?

Accepted Answer

It is always non-negative

Question 13

What is the result of $$\dfrac{(x^3$y^4)^2$}{(x^3$y^4)^3$}$$?

Accepted Answer

$$\dfrac{1}{x^3$y^4$$}$

Question 14

If you have $$2^4$$ 	imes $$2^3$$, what is the result?

Accepted Answer

$$2^7$$

Question 15

Which of the following is the correct simplification for $$\dfrac{(x^3$y^4)^2$}{(x^3$y^4)^3$}$$?

Accepted Answer

$$(x^3y^4$)^{-1}$$

Question 16

If you have $$4.75 	imes 10^5$ and want to express it as a standard number, what is the result?

Accepted Answer

$$475000$$

Question 17

Which of the following is the correct way to divide $$4.75 	imes 10^5$ by 2$$ 	imes $$10^3$$?

Accepted Answer

$$2.375 	imes 10^2$

Question 18

If you have $$7.2 	imes 10$$^{-6}$$, which of the following is the correct standard notation?

Accepted Answer

$$0.0000072$$

Question 19

Which of the following is the correct result for $$2^0$$?

Accepted Answer

$$1$$

Question 20

If you have $$1.23 	imes 10^2$, what is the value in standard notation?

Accepted Answer

$$123$$

Mathematics Review for Physics: Exponents, Scientific Notation, and Algebraic Manipulation

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