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PSAT Math : Exponents

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Example Questions

Example Question #1181 : Psat Mathematics

Simplify:

$\small \left ( 3 - 2i \right )\left ( 2 + i\right )$

Possible Answers:

$\small 6 - 3i$

$\small 6 + 3i$

$\small 6 - i$

$\small 8 - i$

$\small 8 + i$

Correct answer:

$\small 8 - i$

Explanation:

Use the FOIL method that states to multiply the Firsts, Outter, Inner, Lasts. Also remember that $\small i \times i = -1$ :

$\small \left ( 3 - 2i \right )\left ( 2 + i\right )$

$\small = 3 \times 2 + 3 \times i - 2i \times 2 - 2i \times i$

$\small = 6 +3i -4i + 2$

$\small = 8 - i$

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Example Question #1 : How To Find A Ratio Of Exponents

If and are positive integers and , then what is the value of $\frac{m}{n}$ ?

Possible Answers:

$\frac{5}{3}$

$\frac{1}{3}$

$\frac{1}{16}$

Correct answer:

Explanation:

4³= 64

Alternatively written, this is 4(4)(4) = 64 or 4³= 64^1.

Thus, m = 3 and n = 1.

m/n = 3/1 = 3.

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Example Question #2 : How To Find A Ratio Of Exponents

Write the following logarithm in expanded form:

$\log x^{2}y$

Possible Answers:

$2\log x+\log y$

$\log x^{2}+\log y$

$\log x+\log y$

$2\left ( \log xy \right )$

$2\log x-\log y$

Correct answer:

$2\log x+\log y$

Explanation:

$\log x^{2}y=\log x^{2}+\log y=2\log x+\log y$

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Example Question #2 : Exponents And Rational Numbers

Com_exp_1

Which of the following lists the above quantities from least to greatest?

Possible Answers:

II, III, I, IV

I, IV, II, III

I, IV, III, II

I, III, II, IV

IV, III, II, I

Correct answer:

I, III, II, IV

Explanation:

Com_exp_2

Com_exp_3

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Example Question #1 : How To Find An Exponent From A Rational Number

Solve for .

$2^{x}= 64$

Possible Answers:

x=-6

x=64

x=5

x=6

$x=64^{2}$

Correct answer:

x=6

Explanation:

Since $2^{x}= 2^{6}$

Hence x=6

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Example Question #1 : How To Find An Exponent From A Rational Number

Simplify:

$\sqrt[3]{x^{10}y^{8}z^{9}}$

Possible Answers:

$x^{3}y^{3}z^{3}$

$\sqrt[3]{xy^{2}}$

$x^{3}y^{2}z^{3}^{\sqrt[3]{xyz}}$

$x^{3}y^{2}z^{3}\sqrt[3]{xy^{2}}$

$x^{3}y^{2}z^{3}$

Correct answer:

$x^{3}y^{2}z^{3}\sqrt[3]{xy^{2}}$

Explanation:

$\sqrt[3]{x^{9}xy^{6}y^{2}z^{9}}=x^{3}y^{2}z^{3}\sqrt[3]{xy^{2}}$

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Example Question #1 : How To Find An Exponent From A Rational Number

Solve for :

$\sqrt{x} -1= 4$

Possible Answers:

Correct answer:

Explanation:

From the equation one can see that

$\sqrt{x} = 5$

Hence must be equal to 25.

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Example Question #2 : How To Find An Exponent From A Rational Number

Evaluate:

$\log 0.1=$

Possible Answers:

$\frac{1}{10}$

Correct answer:

Explanation:

$0.1= 10^{-1}$

$\log 0.1=-1$

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Example Question #1 : How To Find An Exponent From A Rational Number

Solve for .

$\log_{2}x=4$

Possible Answers:

Correct answer:

Explanation:

$x= 2^4{}= 16$

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Example Question #3 : How To Find An Exponent From A Rational Number

$\log 3=a$

and

$\log 5=b$

Find $\log 15$

Possible Answers:

a+b

$b^{2}$

$a^{2}$

Correct answer:

a+b

Explanation:

$\log 15=\log (5\cdot 3)=\log 5+\log 3$

Hence the correct answer is a+b .

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PSAT Math : Exponents

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #1181 : Psat Mathematics

Example Question #1 : How To Find A Ratio Of Exponents

Example Question #2 : How To Find A Ratio Of Exponents

Example Question #2 : Exponents And Rational Numbers

Example Question #1 : How To Find An Exponent From A Rational Number

Example Question #1 : How To Find An Exponent From A Rational Number

Example Question #1 : How To Find An Exponent From A Rational Number

Example Question #2 : How To Find An Exponent From A Rational Number

Example Question #1 : How To Find An Exponent From A Rational Number

Example Question #3 : How To Find An Exponent From A Rational Number

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