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SSAT Upper Level Math : Algebra

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

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Example Questions

Example Question #13 : Properties Of Exponents

Express the result in scientific notation:

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

Possible Answers:

$1.25 \times 10^{5}$

$8 \times 10^{5}$

$8 \times 10^{6}$

$1.25 \times 10^{6}$

$1.25 \times 10^{7}$

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 #72 : Algebra

Assume all variables to be nonzero.

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

Possible Answers:

24xyz

24xyz - 1

24xyz - 24

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 #14 : Properties Of Exponents

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 #13 : How To Find The Properties Of An Exponent

Express the result in scientific notation:

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

Possible Answers:

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

$2.5 \times 10 ^{-5}$

$4\times 10 ^{ -6}$

$4\times 10 ^{ -4}$

$4\times 10 ^{ -5}$

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 : Properties Of Exponents

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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Example Question #21 : Properties Of Exponents

Which of the values below is equal to $4^{3}$ ?

Possible Answers:

Correct answer:

Explanation:

$4^{3}$ is equal to $4\cdot4\cdot4$

$4\cdot4=16$

Therefore, $4\cdot4\cdot4=16\cdot4=64$

Thus, 64 is the correct answer.

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Example Question #22 : Properties Of Exponents

Which of the values below is equal to $2^{5}$ ?

Possible Answers:

Correct answer:

Explanation:

$2^{5}$ is equal to $2\cdot2\cdot2\cdot2\cdot2$

Given that $2\cdot2=4$ , the above expression can be simplified to:

$4\cdot4\cdot2=16\cdot2=32$

Therefore, 32 is the correct answer.

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Example Question #23 : Properties Of Exponents

Which of the following is equal to 27?

Possible Answers:

$5^{2}$

$3\cdot2^{2}$

$3^{4}$

$3^{3}$

Correct answer:

$3^{3}$

Explanation:

$3^{3}$ is equal to $3\cdot3\cdot3$ .

Given that $3\cdot3=9$ , it follows that

$3\cdot3\cdot3=9\cdot3=27$ .

Therefore, $3^{3}$ is the correct answer.

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Example Question #24 : Properties Of Exponents

Evaluate:

$3^{-2}\times3^{-6}\times3^{6}$

Possible Answers:

$\frac{1}{9}$

$\frac{1}{3}$

Correct answer:

$\frac{1}{9}$

Explanation:

The bases of all three terms are alike. Since the terms are of a specific power, the rule of exponents state that the powers can be added if the terms are multiplied.

$3^{-2}\times3^{-6}\times3^{6}= 3^{-2-6+6}= 3^{-2}$

When we have a negative exponent, we we put the number and the exponent as the denominator, over

$\frac{1}{3^2}=\frac{1}{9}$

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Example Question #25 : Properties Of Exponents

Simplify:

$\frac{8x ^{-2}}{(3x)^{2}}$

Possible Answers:

$\frac{8}{9x}$

$\frac{8}{3x ^{4}}$

$\frac{8}{9}$

$\frac{8}{9x ^{4}}$

$\frac{8}{3}$

Correct answer:

$\frac{8}{9x ^{4}}$

Explanation:

$\frac{8x ^{-2}}{(3x)^{2}}$

To solve this problem, we start with the parentheses and exponents in the denominator.

$= \frac{8x ^{-2}}{3^{2}x^{2}} = \frac{8x ^{-2}}{9x^{2}}$

Next, we can bring the x^2 from the denominator up to the numerator by making the exponent negative.

$= \frac{8x ^{-2-2}}{9} = \frac{8x ^{-4}}{9}$

Finally, to get rid of the negative exponent we can bring it back down to the denominator.

$= \frac{8}{9x ^{4}}$

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SSAT Upper Level Math : Algebra

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #13 : Properties Of Exponents

Example Question #72 : Algebra

Example Question #14 : Properties Of Exponents

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

Example Question #15 : Properties Of Exponents

Example Question #21 : Properties Of Exponents

Example Question #22 : Properties Of Exponents

Example Question #23 : Properties Of Exponents

Example Question #24 : Properties Of Exponents

Example Question #25 : Properties Of Exponents

All SSAT Upper Level Math Resources

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