PSAT Math : How to find an exponent from a rational number

Study concepts, example questions & explanations for PSAT Math

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Example Questions

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

Com_exp_1

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

Possible Answers:

I, IV, II, III

IV, III, II, I

I, IV, III, II

II, III, I, IV

I, III, II, IV

Correct answer:

I, III, II, IV

Explanation:

Com_exp_2

Com_exp_3

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

Solve for .

2^{x}= 64

Possible Answers:

Correct answer:

Explanation:

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

Hence

Example Question #2 : Exponents And Rational Numbers

Simplify:

 

Possible Answers:

Correct answer:

Explanation:

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

Solve for :

Possible Answers:

Correct answer:

Explanation:

From the equation one can see that

Hence  must be equal to 25.

Example Question #4 : Exponents And Rational Numbers

Evaluate:

Possible Answers:

Correct answer:

Explanation:

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

Solve for .

 

Possible Answers:

Correct answer:

Explanation:

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

and

 

Find

Possible Answers:

Correct answer:

Explanation:

Hence the correct answer is .

Example Question #5 : How To Find An Exponent From A Rational Number

Solve for .

Possible Answers:

Correct answer:

Explanation:

Use the rules of logarithms to combine terms.

Hence,

By fatoring we get

Hence .

However, you cannot take the logarithm of a negative number. Thus, the only value for is .

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

If a piece of pie is cut into 3 sections, and each of those pieces is further cut into three sections, then those pieces are cut into three sections, how many (tiny) pieces of pie are there?

Possible Answers:

27

36

40

125

12

Correct answer:

27

Explanation:

The answer is 33 = 27

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

Solve for .

Possible Answers:

Correct answer:

Explanation:

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