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PSAT Math : Exponential Operations

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Example Questions

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Example Question #61 : Exponential Operations

Simplify: $x^{5}\cdot x^{2}$

Possible Answers:

$2x^{7}$

$x^{7}$

$2x^{10}$

$x^{10}$

This expression cannot be simplified any further

Correct answer:

$x^{7}$

Explanation:

When you are multiplying and the bases are the same, you add the exponents together. Because both bases are you add 5+2=7 as your new exponent. You then keep the same base, , to the 7th power.

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Example Question #24 : How To Multiply Exponents

Solve for :

$\sqrt[3]{x-3} = 2$

Possible Answers:

$None\ of\ the\ above$

Correct answer:

Explanation:

$\left ( \sqrt[3]{x-3} \right )^{3} = 2^{3}$

Now the left side equals x-3 and the right side equals 8. Hence:

x-3 = 8

Therefore must be equal to 11.

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Example Question #1 : How To Use Scientific Notation

Express 0.000000076 in scientific notation.

Possible Answers:

$7 6 \times 10^{-9}$

$7.6 \times 10^{-9}$

$0.76\times 10^{-8}$

$7 6 \times 10^{-8}$

$7.6 \times 10^{-8}$

Correct answer:

$7.6 \times 10^{-8}$

Explanation:

Write the number:

$0.000\; 000\; 076$

Counting the number of places, move the decimal point to the right until it is after the first nonzero digit:

$0 \; 000\; 000\; 07.6$

The resulting number is 7.6; the number of places the decimal point moved to the right was 8. In scientific notation, this number is $7.6 \times 10^{-8}$ .

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Example Question #1 : How To Use Scientific Notation

Express the square of $7 \times 10^{15}$ in scientific notation.

Possible Answers:

$4.9 \times 10^{16}$

$4.9 \times 10^{31}$

$49 \times 10^{30}$

$49 \times 10^{225}$

$4.9 \times 10^{226}$

Correct answer:

$4.9 \times 10^{31}$

Explanation:

Take advantage of the exponent rules.

$\left (7 \times 10^{15} \right )^{2}$

$= 7^{2} \times \left ( 10^{15} \right )^{2}$

$= 49 \times 10^{15 \times 2}$

$= 49 \times 10^{30}$

$= 4.9 \times 10^{1} \times 10^{30}$

$= 4.9 \times 10^{1+30}$

$= 4.9 \times 10^{31}$

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Example Question #1 : How To Use Scientific Notation

The number 0.0000279 is equivalent to which of the following?

Possible Answers:

$2.79\cdot 10^{5}$

$2.79\cdot 10^{4}$

$2.79\cdot 10^{-6}$

$2.79\cdot 10^{-4}$

$2.79\cdot 10^{-5}$

Correct answer:

$2.79\cdot 10^{-5}$

Explanation:

Each of the answers to this question are in scientific notation. To determine the exponent on the 10, see how many places you need to move the decimal over to get from your original number to 2.79.

Scientific_notation

Because the decimal place moves 5 places, the exponent will be 5, and because the decimal moves to the RIGHT, the exponent is going to be negative.

So the answer to the quesiton is $2.79\cdot 10^{-5}$

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Example Question #61 : Exponential Operations

Put the following value in scientific notation:

19540000

Possible Answers:

$1.954 \times 10^{6}$

$1.954 \times 10^{7}$

$19.54 \times 10^{7}$

$1954 \times 10^{4}$

Correct answer:

$1.954 \times 10^{7}$

Explanation:

Our first value for scientific notation should be between and . We then multiply this value by raised to a power equal to the number of spaces our decimal has moved to the left.

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PSAT Math : Exponential Operations

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #61 : Exponential Operations

Example Question #24 : How To Multiply Exponents

Example Question #1 : How To Use Scientific Notation

Example Question #1 : How To Use Scientific Notation

Example Question #1 : How To Use Scientific Notation

Example Question #61 : Exponential Operations

All PSAT Math Resources

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