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Common Core: 8th Grade Math : Generate Equivalent Numerical Expressions: CCSS.Math.Content.8.EE.A.1

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

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All Common Core: 8th Grade Math Resources

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Example Questions

Example Question #21 : Expressions & Equations

Solve:

$4^{-8}\times4^{6}$

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

$4^{-8}\times 4^{6}=4^{(-8+6)}$

Solve for the exponents

-8+6=-2

$4^{-2}$

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

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

Report an Error

Example Question #21 : Generate Equivalent Numerical Expressions: Ccss.Math.Content.8.Ee.A.1

Solve:

$2^{-8}\times2^{3}$

Possible Answers:

$-\frac{1}{32}$

$\frac{1}{32}$

Correct answer:

$\frac{1}{32}$

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

$2^{-8}\times 2^{3}=2^{(-8+3)}$

Solve for the exponents

-8+3=-5

$2^{-5}$

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

$\frac{1}{2^{5}}=\frac{1}{32}$

Report an Error

Example Question #23 : Expressions & Equations

Solve:

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

Possible Answers:

$\frac{1}{81}$

$-\frac{1}{81}$

Correct answer:

$\frac{1}{81}$

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

$3^{-6}\times 3^{2}=3^{(-6+2)}$

Solve for the exponents

-6+2=-4

$3^{-4}$

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

$\frac{1}{3^{4}}=\frac{1}{81}$

Report an Error

Example Question #22 : Generate Equivalent Numerical Expressions: Ccss.Math.Content.8.Ee.A.1

Solve:

$3^{-21}\times3^{16}$

Possible Answers:

243

$-\frac{1}{243}$

$\frac{1}{243}$

Correct answer:

$\frac{1}{243}$

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

$3^{-21}\times 3^{16}=3^{(-21+16)}$

Solve for the exponents

-21+16=-5

$3^{-5}$

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

$\frac{1}{3^{5}}=\frac{1}{243}$

Report an Error

Example Question #21 : Generate Equivalent Numerical Expressions: Ccss.Math.Content.8.Ee.A.1

Solve:

$5^{-19}\times5^{17}$

Possible Answers:

$-\frac{1}{27}$

$\frac{1}{25}$

Correct answer:

$\frac{1}{25}$

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

$5^{-19}\times 5^{17}=5^{(-19+17)}$

Solve for the exponents

-19+17=-2

$5^{-2}$

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

$\frac{1}{5^{2}}=\frac{1}{25}$

Report an Error

Example Question #22 : Generate Equivalent Numerical Expressions: Ccss.Math.Content.8.Ee.A.1

Solve:

$9^{-12}\times9^{9}$

Possible Answers:

$\frac{1}{729}$

$\frac{1}{81}$

$\frac{1}{346}$

$\frac{1}{716}$

Correct answer:

$\frac{1}{729}$

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

$9^{-12}\times 9^{9}=9^{(-12+9)}$

Solve for the exponents

-12+9=-3

$9^{-3}$

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

$\frac{1}{9^{3}}=\frac{1}{729}$

Report an Error

Example Question #25 : Expressions & Equations

Which of the following expressions is equivalent to $2^{-13}\times2^{10}$ ?

Possible Answers:

$\frac{1}{8}$

$-\frac{1}{8}$

Correct answer:

$\frac{1}{8}$

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

$2^{-13}\times 2^{10}=2^{(-13+10)}$

Solve for the exponents

-13+10=-3

$2^{-3}$

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

$\frac{1}{2^{3}}=\frac{1}{8}$

Report an Error

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Common Core: 8th Grade Math : Generate Equivalent Numerical Expressions: CCSS.Math.Content.8.EE.A.1

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

All Common Core: 8th Grade Math Resources

Example Questions

Example Question #21 : Expressions & Equations

Example Question #21 : Generate Equivalent Numerical Expressions: Ccss.Math.Content.8.Ee.A.1

Example Question #23 : Expressions & Equations

Example Question #22 : Generate Equivalent Numerical Expressions: Ccss.Math.Content.8.Ee.A.1

Example Question #21 : Generate Equivalent Numerical Expressions: Ccss.Math.Content.8.Ee.A.1

Example Question #22 : Generate Equivalent Numerical Expressions: Ccss.Math.Content.8.Ee.A.1

Example Question #25 : Expressions & Equations

All Common Core: 8th Grade Math Resources

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