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Common Core: 8th Grade Math : Expressions & Equations

Study concepts, example questions & explanations for Common Core: 8th Grade Math

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All Common Core: 8th Grade Math Resources

7 Diagnostic Tests 75 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #2 : Properties Of Exponents

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

Possible Answers:

$\dpi{100} 243$

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

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

$\dpi{100} 729$

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 #63 : Ssat Upper Level Quantitative (Math)

Evaluate:

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

Possible Answers:

$\frac{1}{2}$

The quantity is undefined.

$\frac{1}{256}$

$-\frac{1}{2}$

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 #9 : Properties Of Exponents

Evaluate:

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

Possible Answers:

100,000,000

100

The expression is undefined.

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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Example Question #11 : Properties Of Exponents

Evaluate:

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

Possible Answers:

16,000

The expression is undefined.

-160,000

160,000

-16,000

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 #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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Example Question #12 : Generate Equivalent Numerical Expressions: Ccss.Math.Content.8.Ee.A.1

Solve:

$3^{-5}\times3^{2}$

Possible Answers:

$\frac{1}{27}$

$\frac{1}{9}$

Correct answer:

$\frac{1}{27}$

Explanation:

In order to solve this problem, we need to recall our exponent rules:

When our base numbers are equal to each other, like in this problem, we can add our exponents together using the following formula:

$a^m\times a^n=a^{(m+n)}$

Let's apply this rule to our problem

$3^{-5}\times 3^{2}=3^{(-5+2)}$

Solve for the exponents

-5+2=-3

$3^{-3}$

We cannot leave this problem in this format because we cannot have a negative exponent. Instead, we can move the base and the exponent to the denominator of a fraction:

$a^{(-m)}=\frac{1}{a^m}$

Solve the problem

$\frac{1}{3^{3}}=\frac{1}{27}$

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Example Question #13 : Generate Equivalent Numerical Expressions: Ccss.Math.Content.8.Ee.A.1

Solve:

$2^{-7}\times2^{5}$

Possible Answers:

$-\frac{1}{4}$

$\frac{1}{4}$

Correct answer:

$\frac{1}{4}$

Explanation:

In order to solve this problem, we need to recall our exponent rules:

When our base numbers are equal to each other, like in this problem, we can add our exponents together using the following formula:

$a^m\times a^n=a^{(m+n)}$

Let's apply this rule to our problem

$2^{-7}\times 2^{5}=2^{(-7+5)}$

Solve for the exponents

-7+5=-2

$2^{-2}$

We cannot leave this problem in this format because we cannot have a negative exponent. Instead, we can move the base and the exponent to the denominator of a fraction:

$a^{(-m)}=\frac{1}{a^m}$

Solve the problem

$\frac{1}{2^{2}}=\frac{1}{4}$

Report an Error

Example Question #14 : Generate Equivalent Numerical Expressions: Ccss.Math.Content.8.Ee.A.1

Solve:

$2^{-8}\times2^{4}$

Possible Answers:

$-\frac{1}{16}$

$\frac{1}{16}$

Correct answer:

$\frac{1}{16}$

Explanation:

In order to solve this problem, we need to recall our exponent rules:

When our base numbers are equal to each other, like in this problem, we can add our exponents together using the following formula:

$a^m\times a^n=a^{(m+n)}$

Let's apply this rule to our problem

$2^{-8}\times 2^{4}=2^{(-8+4)}$

Solve for the exponents

-8+4=-4

$2^{-4}$

We cannot leave this problem in this format because we cannot have a negative exponent. Instead, we can move the base and the exponent to the denominator of a fraction:

$a^{(-m)}=\frac{1}{a^m}$

Solve the problem

$\frac{1}{2^{4}}=\frac{1}{16}$

Report an Error

Example Question #15 : Generate Equivalent Numerical Expressions: Ccss.Math.Content.8.Ee.A.1

Solve:

$3^{-11}\times3^{9}$

Possible Answers:

$\frac{1}{9}$

$-\frac{1}{9}$

Correct answer:

$\frac{1}{9}$

Explanation:

In order to solve this problem, we need to recall our exponent rules:

When our base numbers are equal to each other, like in this problem, we can add our exponents together using the following formula:

$a^m\times a^n=a^{(m+n)}$

Let's apply this rule to our problem

$3^{-11}\times 3^{9}=3^{(-11+9)}$

Solve for the exponents

-11+9=-2

$3^{-2}$

We cannot leave this problem in this format because we cannot have a negative exponent. Instead, we can move the base and the exponent to the denominator of a fraction:

$a^{(-m)}=\frac{1}{a^m}$

Solve the problem

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

Report an Error

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All Common Core: 8th Grade Math Resources

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Common Core: 8th Grade Math : Expressions & Equations

Study concepts, example questions & explanations for Common Core: 8th Grade Math

All Common Core: 8th Grade Math Resources

Example Questions

Example Question #2 : Properties Of Exponents

Example Question #63 : Ssat Upper Level Quantitative (Math)

Example Question #9 : Properties Of Exponents

Example Question #11 : Properties Of Exponents

Example Question #24 : Properties Of Exponents

Example Question #25 : Properties Of Exponents

Example Question #12 : Generate Equivalent Numerical Expressions: Ccss.Math.Content.8.Ee.A.1

Example Question #13 : Generate Equivalent Numerical Expressions: Ccss.Math.Content.8.Ee.A.1

Example Question #14 : Generate Equivalent Numerical Expressions: Ccss.Math.Content.8.Ee.A.1

Example Question #15 : Generate Equivalent Numerical Expressions: Ccss.Math.Content.8.Ee.A.1

All Common Core: 8th Grade Math Resources

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