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SSAT Upper Level Math : Algebra

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 #105 : Write And Evaluate Numerical Expressions With Exponents: Ccss.Math.Content.6.Ee.A.1

What is $18\times18\times18\times18\times18$ in exponential notation?

Possible Answers:

$5^{18}$

$18\times5$

18^5

$5\times5\times5\times5\times5\times5\times5\times5\times5\times5\times5\times5$

$5\times18$

Correct answer:

18^5

Explanation:

Exponential notation includes a base number and an exponent. The base number is the number that is being multiplied and the exponent is how many times the base number is being multiplied to itself.

In this case, is our base number and it's being multiplied to itself times, so that is our exponent.

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Example Question #106 : Write And Evaluate Numerical Expressions With Exponents: Ccss.Math.Content.6.Ee.A.1

What is $19\times19\times19\times19$ in exponential notation?

Possible Answers:

$4^{19}$

$4\times4\times4\times4\times4\times4\times4\times4$

$4\times19$

$19\times4$

19^4

Correct answer:

19^4

Explanation:

Exponential notation includes a base number and an exponent. The base number is the number that is being multiplied and the exponent is how many times the base number is being multiplied to itself.

In this case, is our base number and it's being multiplied to itself times, so that is our exponent.

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Example Question #107 : Write And Evaluate Numerical Expressions With Exponents: Ccss.Math.Content.6.Ee.A.1

What is $20\times20\times20\times20\times20\times20$ in exponential notation?

Possible Answers:

20^6

$20\times6$

$6\times6\times6\times6$

$6\times20$

$6^{20}$

Correct answer:

20^6

Explanation:

Exponential notation includes a base number and an exponent. The base number is the number that is being multiplied and the exponent is how many times the base number is being multiplied to itself.

In this case, is our base number and it's being multiplied to itself times, so that is our exponent.

Report an Error

Example Question #108 : Write And Evaluate Numerical Expressions With Exponents: Ccss.Math.Content.6.Ee.A.1

What is $21\times21\times21\times21\times21\times21\times21\times21\times21$ in exponential notation?

Possible Answers:

21^9

$9^{21}$

$9\times9\times9\times9\times9\times9\times9\times9\times9\times9\times9\times9$

$21\times9$

$9\times21$

Correct answer:

21^9

Explanation:

Exponential notation includes a base number and an exponent. The base number is the number that is being multiplied and the exponent is how many times the base number is being multiplied to itself.

In this case, is our base number and it's being multiplied to itself times, so that is our exponent.

Report an Error

Example Question #109 : Write And Evaluate Numerical Expressions With Exponents: Ccss.Math.Content.6.Ee.A.1

What is $22\times22\times22\times22\times22\times22\times22\times22$ in exponential notation?

Possible Answers:

$22\times8$

22^8

$8\times8\times8\times8\times8\times8$

$8\times22$

$8^{22}$

Correct answer:

22^8

Explanation:

Exponential notation includes a base number and an exponent. The base number is the number that is being multiplied and the exponent is how many times the base number is being multiplied to itself.

In this case, is our base number and it's being multiplied to itself times, so that is our exponent.

Report an Error

Example Question #101 : Write And Evaluate Numerical Expressions With Exponents: Ccss.Math.Content.6.Ee.A.1

What is $23\times23\times23\times23\times23\times23$ in exponential notation?

Possible Answers:

23^6

$6\times23$

$23\times6$

$6^{23}$

$6\times6\times6\times6\times6\times6\times6\times6\times6\times6\times6$

Correct answer:

23^6

Explanation:

Exponential notation includes a base number and an exponent. The base number is the number that is being multiplied and the exponent is how many times the base number is being multiplied to itself.

In this case, is our base number and it's being multiplied to itself times, so that is our exponent.

Report an Error

Example Question #121 : Properties Of Exponents

$x^{5} = - 77$

y = -2

$(xy) ^{5} =?$

Possible Answers:

- 2,464

2,464

Correct answer:

2,464

Explanation:

Apply the Power of a Product Principle:

$(xy) ^{5} = x^{5} y ^{5}$

Setting $x^{5} = - 77$ and y = -2 , keeping in mind that an odd power of a negative number is negative:

$x^{5} y ^{5}$

$= -77 \cdot (-2 ) ^{5}$

$= -77 \cdot[ - (2 ^{5} )]$

$= -77 \cdot (-32)$

$= + (77 \cdot 32)$

= 2,464

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Example Question #123 : How To Find The Properties Of An Exponent

y > 0 and z> 0

$y^{2} = 12$

$z^{2} = 5$

Evaluate $(y z)^{3}$ .

Possible Answers:

$12\sqrt{30}$

$12\sqrt{15}$

$120 \sqrt{30 }$

$120 \sqrt{15}$

Correct answer:

$120 \sqrt{15}$

Explanation:

$y^{2} = 12$ and is positive, so

$y = \sqrt{12}$ .

The greatest perfect square factor of 12 is 4, so the radical can be simplified:

$y = \sqrt{4} \cdot \sqrt{3} = 2 \sqrt{3}$

$z^{2} = 5$ , and is positive, so $z = \sqrt{5}$

By the Power of a Power Property,

$(y z)^{3}$

$= y^{3} z^{3}$

It is easiest to note that this can be broken up by the Product of Powers Principle, and evaluated by substitution:

$y^{3} z^{3}$

$= y^{2+ 1} z^{2+ 1}$

$= y^{2 } \cdot y \cdot z^{2 } \cdot z$

$=12 \cdot \sqrt{12} \cdot 5 \cdot \sqrt{5}$

$=12 \cdot 5 \cdot \sqrt{12} \cdot \sqrt{5}$

$=60 \cdot \sqrt{60}$

The greatest perfect square factor of 60 is 4, so the radical can be simplified:

$60 \cdot \sqrt{60}$

$=60 \cdot \sqrt{4} \cdot \sqrt{15}$

$=60 \cdot 2 \cdot \sqrt{15}$

$=120 \sqrt{15}$

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Example Question #122 : Properties Of Exponents

$x^{2} = 75$

$y^{2} = 3$

and are both positive.

Evaluate (4x +y) (4x -y) .

Possible Answers:

1,197

1,083

297

183

Correct answer:

1,197

Explanation:

By the difference of squares pattern:

(4x +y) (4x -y)

$= (4x) ^{2} - y^{2}$

By the Power of a Power Principle,

$(4x) ^{2} - y^{2}$

$= 4^{2}x^{2} - y^{2}$

$=16 x^{2} - y^{2}$

Substituting 75 and 3 for $x^{2}$ and $y^{2}$ , respectively:

=16 (75)- 3

=1,200- 3

=1,197

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Example Question #121 : How To Find The Properties Of An Exponent

$y ^{5} = -7$

$y^{20} = ?$

Possible Answers:

2,401

-2,401

Correct answer:

2,401

Explanation:

By the Power of a Power Principle,

$(y ^{5} ) ^{4} = y ^{5 \cdot 4} = y ^{20}$

Substituting for $y ^{5}$ , keeping in mind that an even power of any number must be positive:

$y ^{20} = (y ^{5} ) ^{4} =( -7)^{4} = 7 ^{4} = 7 \cdot 7 \cdot 7 \cdot 7= 2,401$

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All SSAT Upper Level Math Resources

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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 #105 : Write And Evaluate Numerical Expressions With Exponents: Ccss.Math.Content.6.Ee.A.1

Example Question #106 : Write And Evaluate Numerical Expressions With Exponents: Ccss.Math.Content.6.Ee.A.1

Example Question #107 : Write And Evaluate Numerical Expressions With Exponents: Ccss.Math.Content.6.Ee.A.1

Example Question #108 : Write And Evaluate Numerical Expressions With Exponents: Ccss.Math.Content.6.Ee.A.1

Example Question #109 : Write And Evaluate Numerical Expressions With Exponents: Ccss.Math.Content.6.Ee.A.1

Example Question #101 : Write And Evaluate Numerical Expressions With Exponents: Ccss.Math.Content.6.Ee.A.1

Example Question #121 : Properties Of Exponents

Example Question #123 : How To Find The Properties Of An Exponent

Example Question #122 : Properties Of Exponents

Example Question #121 : How To Find The Properties Of An Exponent

All SSAT Upper Level Math Resources

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