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Common Core: 8th Grade Math : Grade 8

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 : Expressions & Equations

Simplify.

$(x^4)^{6}$

Possible Answers:

$x^{-2}$

$x^{24}$

x^2

$x^{10}$

$x^{46}$

Correct answer:

$x^{24}$

Explanation:

When an exponent is being raised by another exponent, we just multiply the powers of the exponents and keep the base the same.

$(x^4)^{6}=x^{4*6}=x^{24}$

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

Simplify.

$(x^{-3})^{-4}$

Possible Answers:

$x^{34}$

$x^{-7}$

$x^{7}$

$x^{12}$

$x^{-12}$

Correct answer:

$x^{12}$

Explanation:

When an exponent is being raised by another exponent, we just multiply the powers of the exponents and keep the base the same.

$(x^{-3})^{-4}=x^{-3*-4}=x^{12}$

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Example Question #21 : Distributing Exponents (Power Rule)

Simplify.

$(\frac{x^5}{y^3})^3$

Possible Answers:

$\frac{x^{8}}{y^6}$

$\frac{x^{15}}{y^8}$

$\frac{x^{15}}{y^9}$

$\frac{x^{15}}{y^{13}}$

$\frac{x^{15}}{y^3}$

Correct answer:

$\frac{x^{15}}{y^9}$

Explanation:

When an exponent is being raised by another exponent, we just multiply the powers of the exponents and keep the base the same.

$(\frac{x^5}{y^3})^{3}=\frac{x^{5*3}}{y^{3*3}}=\frac{x^{15}}{y^{9}}$

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Example Question #21 : Distributing Exponents (Power Rule)

Simplify the expression $\left ( 2x^3\right )^5$

Possible Answers:

$2x^{15}$

$32x^{15}$

2x^8

$32768x^{15}$

32x^8

Correct answer:

$32x^{15}$

Explanation:

$\left ( 2x^5\right )^3=\left ( 2x^5\right )\left ( 2x^5\right )\left ( 2x^5\right )$

$8x^{15}$

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Example Question #1 : Properties Of Exponents

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

Possible Answers:

$\dpi{100} 200$

$\dpi{100} 4$

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

$\dpi{100} 2$

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 #4 : Expressions & Equations

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

Possible Answers:

$\dpi{100} 32$

$\dpi{100} 16$

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

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 #2 : Properties Of Exponents

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

Possible Answers:

$\dpi{100} 729$

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

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

$\dpi{100} 243$

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 #7 : Properties Of Exponents

Evaluate:

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

Possible Answers:

$\frac{1}{256}$

$\frac{1}{2}$

$-\frac{1}{2}$

The quantity is undefined.

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 #3 : 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 : Expressions & Equations

Evaluate:

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

Possible Answers:

-160,000

The expression is undefined.

16,000

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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All Common Core: 8th Grade Math Resources

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Common Core: 8th Grade Math : Grade 8

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

All Common Core: 8th Grade Math Resources

Example Questions

Example Question #2 : Expressions & Equations

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

Example Question #21 : Distributing Exponents (Power Rule)

Example Question #21 : Distributing Exponents (Power Rule)

Example Question #1 : Properties Of Exponents

Example Question #4 : Expressions & Equations

Example Question #2 : Properties Of Exponents

Example Question #7 : Properties Of Exponents

Example Question #3 : Properties Of Exponents

Example Question #11 : Expressions & Equations

All Common Core: 8th Grade Math Resources

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