SSAT Upper Level Math : How to find the properties of an exponent

Study concepts, example questions & explanations for SSAT Upper Level Math

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Example Questions

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Example Question #2 : Expressions & Equations

Evaluate \dpi{100} \frac{2^{10}}{2^{8}}

Possible Answers:

\dpi{100} \frac{8}{5}

\dpi{100} 4

\dpi{100} 2

\dpi{100} 200

Correct answer:

\dpi{100} 4

Explanation:

If you divide two exponential expressions with the same base, you can simply subtract the exponents.  Here, both the top and the bottom have a base of 2 raised to a power.

So \dpi{100} \frac{2^{10}}{2^{8}}=2^{10-8}=2^{2}=4

Example Question #1 : How To Find The Properties Of An Exponent

\dpi{100} 2^{3}\cdot 2^{2}

Possible Answers:

\dpi{100} 2^{6}

\dpi{100} 16

\dpi{100} 32

Correct answer:

\dpi{100} 32

Explanation:

Since the two expressions have the same base, we just add the exponents.

\dpi{100} 2^{3}\cdot 2^{2}=2^{3+2}=2^{5}=32

Example Question #3 : Properties Of Exponents

Evaluate: \dpi{100} (3^{3})^{2}

Possible Answers:

\dpi{100} 3^{5}

\dpi{100} 3^{6}

\dpi{100} 729

\dpi{100} 243

Correct answer:

\dpi{100} 3^{6}

Explanation:

A power raised to a power indicates that you multiply the two powers.

\dpi{100} (3^{3})^{2}=3^{3\cdot 2}=3^{6}

Example Question #4 : Properties Of Exponents

\dpi{100} Evaluate: (0.50^{2})

Possible Answers:

\dpi{100} 25

\dpi{100} 0.25

\dpi{100} 1

\dpi{100} 2.5

Correct answer:

\dpi{100} 0.25

Explanation:

We can either write \dpi{100} 0.5\times 0.5, or we can convert this to a fraction and write

\dpi{100} \frac{1}{2}\times \frac{1}{2}

\dpi{100} \frac{1}{2}\times \frac{1}{2}=\frac{1\times 1}{2\times 2}=\frac{1}{4}

\dpi{100} \frac{1}{4} in decimal form is 0.25.

Example Question #1 : How To Find The Properties Of An Exponent

\dpi{100} (0.75)^{2}=

Possible Answers:

\dpi{100} \frac{9}{16}

\dpi{100} 49.5

\dpi{100} 5.85

\dpi{100} 58.5

Correct answer:

\dpi{100} \frac{9}{16}

Explanation:

Convert .75 to a fraction. \dpi{100} \frac{75}{100}=\frac{3}{4}.

Now multiply \dpi{100} \frac{3}{4}\times \frac{3}{4}=\frac{3\times 3}{4\times 4}=\frac{9}{16}

Example Question #2 : How To Find The Properties Of An Exponent

 

Possible Answers:

Correct answer:

Explanation:

Therefore, 

Example Question #3 : How To Find The Properties Of An Exponent

Express 0.00000000000097 in scientific notation.

Possible Answers:

Correct answer:

Explanation:

To rewrite a very small number in scientific notation:

Write the number.

Move the decimal point right as many places as needed until it follows the first nonzero digit, which here is the nine. Count the number of places it is moved - here it will be thirteen places.

The number formed is , which will be placed in front; , the negative of the number of places counted, will be the exponent. The number, in scientific notation, will be  .

Example Question #1 : How To Find The Properties Of An Exponent

Evaluate:

Possible Answers:

The quantity is undefined.

Correct answer:

The quantity is undefined.

Explanation:

This is an undefined quantity.

Example Question #61 : Ssat Upper Level Quantitative (Math)

Evaluate:

Possible Answers:

The quantity is undefined.

Correct answer:

Explanation:

Example Question #61 : Algebra

Evaluate:

Possible Answers:

The expression is undefined.

Correct answer:

Explanation:

as 0 taken to any positive power is equal to 0.

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