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SSAT Upper Level Math : Properties of Exponents

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Example Questions

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Example Question #61 :Algebra

Evaluate:

$(80 - 4 \cdot 25) ^{100 \div 25 }$

Possible Answers:

160,000

-160,000

-16,000

16,000

The expression is undefined.

Correct answer:

160,000

Explanation:

$(80 - 4 \cdot 25) ^{100 \div 25 }$

$= (80 - 100) ^{4 }$

$= (-20) ^{4 }$

= (-20) (-20) (-20) (-20) = 160,000

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Example Question #62 :Algebra

If $\dpi{100} x=\sqrt{34}$ then

Possible Answers:

x< 5

6< x< 7

x=4.56

5< x< 6

Correct answer:

5< x< 6

Explanation:

$\dpi{100} \sqrt{25}=5$

$\dpi{100} \sqrt{36}=6$

34 is between 25 and 36, thus its square root must be between the square roots of 25 and 36. x must be a number between 5 and 6.

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Example Question #63 :Algebra

Express the result in scientific notation:

$\left ( 3 \times 10 ^{4}\right )^{3}$

Possible Answers:

$2.7 \times 10 ^{13}$

$9\times 10 ^{7}$

$27 \times 10 ^{12}$

$9\times 10 ^{12}$

$2.7 \times 10 ^{8}$

Correct answer:

$2.7 \times 10 ^{13}$

Explanation:

Applying the power of a product property of exponents, then the power of a power property:

$\left ( 3 \times 10 ^{4}\right )^{3} = 3^{3}\times\left ( 10 ^{4}\right )^{3} = 27 \times 10 ^{4 \times3} = 27 \times 10 ^{12}$

This is not in scientific notation, so we adjust it as follows, applying the product of powers property:

$27 \times 10 ^{12} = 2.7 \times 10 ^{1} \times 10 ^{12} = 2.7 \times 10 ^{1+ 12} =2.7 \times 10 ^{13}$

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Example Question #64 :Algebra

Assume all variables to be nonzero.

Simplify: $4 \left ( xyz \right ) ^{3} (xyz) ^{0}$

Possible Answers:

$12 x^{3}y ^{3}z^{3}$

$64 x^{3}y ^{3}z^{3}$

$4 x^{3}y ^{3}z^{3}$

Correct answer:

$4 x^{3}y ^{3}z^{3}$

Explanation:

Since any nonzero expression taken to the power of 0 is equal to 1,

$4 \left ( xyz \right ) ^{3} (xyz) ^{0} = 4 \left ( xyz \right ) ^{3} \cdot 1 = 4 \left ( xyz \right ) ^{3}$

Using the power of a product property of exponents, this becomes

$4 \left ( xyz \right ) ^{3} = 4 x^{3}y^{3}z^{3}$

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Example Question #65 :Algebra

Express the result in scientific notation:

$(2 \times 10^{3}) (3 \times 10^{4}) (5 \times 10^{5})$

Possible Answers:

$30 \times 10^{12}$

$3 \times 10^{61}$

$3 \times 10^{12}$

$30 \times 10^{60}$

$3 \times 10^{13}$

Correct answer:

$3 \times 10^{13}$

Explanation:

Apply the product of powers property:

$(2 \times 10^{3}) (3 \times 10^{4}) (5 \times 10^{5})$

$= 2 \times 3 \times 5 \times 10^{3} \times 10^{4} \times 10^{5}$

$= 30 \times 10^{3+4+5}$

$= 30 \times 10^{12}$

Since this is not in scientific notation, adjust as follows:

$30 \times 10^{12}$

$= 3 \times 10^{1} \times 10^{12}$

$= 3 \times 10^{1+12}$

$= 3 \times 10^{13}$

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Example Question #11 :How To Find The Properties Of An Exponent

Express the result in scientific notation:

$\frac{1}{1.25 \times 10^{-6}}$

Possible Answers:

$1.25 \times 10^{7}$

$1.25 \times 10^{6}$

$8 \times 10^{5}$

$8 \times 10^{6}$

$1.25 \times 10^{5}$

Correct answer:

$8 \times 10^{5}$

Explanation:

Rewriting the numeator and applying the quotient of powers property:

$\frac{1}{1.25 \times 10^{-6}}$

$= \frac{1 \times 10^{0}}{1.25 \times 10^{-6}}$

$= \frac{1 }{1.25 } \times \frac{ 10^{0}}{ 10^{-6}}$

$=0.8 \times 10^{0- (-6)}$

$=0.8 \times 10^{6}$

This is not in scientific notation, so we adjust it as follows, applying the product of powers property:

$0.8 \times 10^{6}$

$=8 \times 10^{-1} \times 10^{6}$

$=8 \times 10^{-1+6}$

$=8 \times 10^{5}$

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Example Question #12 :How To Find The Properties Of An Exponent

Assume all variables to be nonzero.

Simplify: $4 \left ( 6xyz \right ) ^{1} - \left (24xyz \right )^{0}$

Possible Answers:

24xyz - 24

24xyz

24xyz - 1

Correct answer:

24xyz - 1

Explanation:

Any expression raised to the first power is equal to that expression, and any expression raised to the power of 0 is equal to 1, so

$4 \left ( 6xyz \right ) ^{1} - \left (24xyz \right )^{0}$

$= 4 \left ( 6xyz \right ) -1$

= 24xyz -1

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Example Question #13 :How To Find The Properties Of An Exponent

Assume all variables to be nonzero.

Simplify: $6 (xyz)^{0} + 4(xyz)^{0}$

Possible Answers:

10xyz

24xyz

Correct answer:

Explanation:

Any nonzero expression to the power of zero is equal to 1:

$6 (xyz)^{0} + 4(xyz)^{0} = 6 \times 1 + 4 \times 1 = 6 + 4 = 10$

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Example Question #14 :How To Find The Properties Of An Exponent

Express the result in scientific notation:

$\frac{1}{2.5 \times 10 ^{5}}$

Possible Answers:

$4\times 10 ^{ -6}$

$4\times 10 ^{ -5}$

$4\times 10 ^{ -4}$

$-2.5 \times 10 ^{-5}$

$2.5 \times 10 ^{-5}$

Correct answer:

$4\times 10 ^{ -6}$

Explanation:

Rewriting the numerator and applying the quotient of powers property:

$\frac{1}{2.5 \times 10 ^{5}}$

$= \frac{1\times 10 ^{0}}{2.5 \times 10 ^{5}}$

$= \frac{1 }{2.5 } \times \frac{ 10 ^{0}}{ 10 ^{5}}$

$= 0.4 \times 10 ^{0-5}$

$= 0.4 \times 10 ^{ -5}$

Since this is not in scientific notation, adjust as follows:

$0.4 \times 10 ^{ -5}$

$= 4\times 10 ^{ -1} \times 10 ^{ -5}$

$= 4\times 10 ^{ -1 + (-5)}$

$= 4\times 10 ^{ -6}$

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Example Question #15 :How To Find The Properties Of An Exponent

What is the value of $\frac{6\cdot5^{9}}{2\cdot 5^{7}}$

Possible Answers:

Correct answer:

Explanation:

To solve $\frac{6\cdot5^{9}}{2\cdot 5^{7}}$ , 6 should be divided by 3. The exponent will be equal to the exponent of the numerator minus the exponent of the denominator. This results in:

$3\cdot5^{2}$

$3\cdot25$

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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 #61 :Algebra

Example Question #62 :Algebra

Example Question #63 :Algebra

Example Question #64 :Algebra

Example Question #65 :Algebra

Example Question #11 :How To Find The Properties Of An Exponent

Example Question #12 :How To Find The Properties Of An Exponent

Example Question #13 :How To Find The Properties Of An Exponent

Example Question #14 :How To Find The Properties Of An Exponent

Example Question #15 :How To Find The Properties Of An Exponent

All SSAT Upper Level Math Resources

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