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SSAT Upper Level Math : Properties of Exponents

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

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All SSAT Upper Level Math Resources

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Example Questions

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

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

Possible Answers:

$\dpi{100} 4$

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

$\dpi{100} 2$

$\dpi{100} 200$

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

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

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

Possible Answers:

$\dpi{100} 16$

$\dpi{100} 2^{6}$

$\dpi{100} 32$

Correct answer:

$\dpi{100} 32$

Explanation:

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

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

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

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

Possible Answers:

$\dpi{100} 729$

$\dpi{100} 243$

$\dpi{100} 3^{5}$

$\dpi{100} 3^{6}$

Correct answer:

$\dpi{100} 3^{6}$

Explanation:

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

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

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Example Question #4 : How To Find The Properties Of An Exponent

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

Possible Answers:

$\dpi{100} 25$

$\dpi{100} 2.5$

$\dpi{100} 1$

$\dpi{100} 0.25$

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.

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Example Question #5 : 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 $\dpi{100} \frac{3}{4}\times \frac{3}{4}=\frac{3\times 3}{4\times 4}=\frac{9}{16}$

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Example Question #6 : How To Find The Properties Of An Exponent

$(-4)^{2} + (-4)^{3}$

Possible Answers:

-1,024

Correct answer:

Explanation:

$(-4)^{2} = -4 \cdot (-4) = +(4\cdot 4) = 16$

$(-4)^{3} = -4 \cdot (-4)\cdot (-4) = 16 \cdot (-4) = - (16 \cdot 4) = -64$

Therefore,

$(-4)^{2} + (-4)^{3} = 16 + (-64) = - (64-16) = -48$

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Example Question #7 : How To Find The Properties Of An Exponent

Express 0.00000000000097 in scientific notation.

Possible Answers:

$0.97 \times 10 ^{-12}$

$97 \times 10 ^{-14}$

$9.7 \times 10 ^{-13}$

$0.97 \times 10 ^{-13}$

$9.7 \times 10 ^{-12}$

Correct answer:

$9.7 \times 10 ^{-13}$

Explanation:

To rewrite a very small number in scientific notation:

Write the number.

0.00000000000097

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 9.7 , 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 $9.7 \times 10 ^{-13}$ .

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Example Question #8 : How To Find The Properties Of An Exponent

Evaluate:

$\frac{\left ( -5\right ) ^{5} - 5^{5}}{\left ( -5\right ) ^{5} + 5^{5}}$

Possible Answers:

-6,250

$-\frac{2}{3,125}$

The quantity is undefined.

$-\frac{1}{6,250}$

Correct answer:

The quantity is undefined.

Explanation:

$5^{5} = 5 \times 5 \times 5 \times 5 \times 5 = 3,125$

$\left (-5 \right ) ^{5} = -\left ( 5^{5} \right ) = -3,125$

$\frac{\left ( -5\right ) ^{5} - 5^{5}}{\left ( -5\right ) ^{5} + 5^{5}} = \frac{-3,125 -3,125}{-3,125 + 3,125} =\frac{-6,250}{0}$

This is an undefined quantity.

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Example Question #9 : How To Find The Properties Of An Exponent

Evaluate:

$\frac{4^{4}}{4^{4} +\left ( -4 \right ) ^{4} }$

Possible Answers:

The quantity is undefined.

$\frac{1}{256}$

$-\frac{1}{2}$

$\frac{1}{2}$

Correct answer:

$\frac{1}{2}$

Explanation:

$4^{4} = 4 \times 4 \times 4 \times 4 = 256$

$\left (- 4 \right ) ^{4} = \left (- 4 \right ) \times \left (- 4 \right ) \times \left (- 4 \right ) \times \left (- 4 \right ) = 256$

$\frac{4^{4}}{4^{4} +\left ( -4 \right ) ^{4} } = \frac{256 }{256 + 256} = \frac{256 }{512} =\frac{1 }{2}$

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Example Question #10 : How To Find The Properties Of An Exponent

Evaluate:

$(100 - 4 \cdot 25) ^{100 \div 25 }$

Possible Answers:

The expression is undefined.

100,000,000

100

Correct answer:

Explanation:

$(100 - 4 \cdot 25) ^{100 \div 25 } = (100 - 100) ^{4} = 0 ^{4} =0$

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

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SSAT Upper Level Math : Properties of Exponents

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

All SSAT Upper Level Math Resources

Example Questions

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

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

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

Example Question #4 : How To Find The Properties Of An Exponent

Example Question #5 : How To Find The Properties Of An Exponent

Example Question #6 : How To Find The Properties Of An Exponent

Example Question #7 : How To Find The Properties Of An Exponent

Example Question #8 : How To Find The Properties Of An Exponent

Example Question #9 : How To Find The Properties Of An Exponent

Example Question #10 : How To Find The Properties Of An Exponent

All SSAT Upper Level Math Resources

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