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Algebra II : Exponents

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #211 : Exponents

Evaluate:

4^4 $\displaystyle 4^4$

Possible Answers:

$\displaystyle 64$

$\displaystyle 44$

$\displaystyle 16$

1024 $\displaystyle 1024$

256 $\displaystyle 256$

Correct answer:

256 $\displaystyle 256$

Explanation:

4^4 $\displaystyle 4^4$ is expanded to 4*4*4*4 $\displaystyle 4*4*4*4$ .

We will simply multiply the values in order to get the answer:

256 $\displaystyle 256$

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Example Question #682 : Mathematical Relationships And Basic Graphs

Expand:

$5^{-4}$ $\displaystyle 5^{-4}$

Possible Answers:

$\displaystyle 5*4*-5*-4$

$\displaystyle -5*-5*-5*-5$

$\displaystyle 4*4*4*4*4$

-5*4 $\displaystyle -5*4$

$\frac{1}{5}*\frac{1}{5}*\frac{1}{5}*\frac{1}{5}$ $\displaystyle \frac{1}{5}*\frac{1}{5}*\frac{1}{5}*\frac{1}{5}$

Correct answer:

$\frac{1}{5}*\frac{1}{5}*\frac{1}{5}*\frac{1}{5}$ $\displaystyle \frac{1}{5}*\frac{1}{5}*\frac{1}{5}*\frac{1}{5}$

Explanation:

When exponents are negative, we can express them usinf the following format: $x^{-a}=\frac{1}{x^a}$ $\displaystyle x^{-a}=\frac{1}{x^a}$

in this formula, $\displaystyle a$ is a positive exponent and $\displaystyle x$ is the base.

We can express $5^{-4}$ $\displaystyle 5^{-4}$ as $(5^{-1})^4$ $\displaystyle (5^{-1})^4$ , which is also the same as:

$\frac{1}{5}*\frac{1}{5}*\frac{1}{5}*\frac{1}{5}$ $\displaystyle \frac{1}{5}*\frac{1}{5}*\frac{1}{5}*\frac{1}{5}$

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Example Question #212 : Exponents

Evaluate:

$8^{-3}$ $\displaystyle 8^{-3}$

Possible Answers:

512 $\displaystyle 512$

$-\frac{1}{512}$ $\displaystyle -\frac{1}{512}$

$\displaystyle -24$

$\frac{1}{512}$ $\displaystyle \frac{1}{512}$

$\displaystyle -512$

Correct answer:

$\frac{1}{512}$ $\displaystyle \frac{1}{512}$

Explanation:

When exponents are negative, we can express them usinf the following format: $x^{-a}=\frac{1}{x^a}$ $\displaystyle x^{-a}=\frac{1}{x^a}$

in this formula, $\displaystyle a$ is a positive exponent and $\displaystyle x$ is the base.

Therefore:

$8^{-3}=\frac{1}{8}*\frac{1}{8}*\frac{1}{8}=\frac{1}{512}$ $\displaystyle 8^{-3}=\frac{1}{8}*\frac{1}{8}*\frac{1}{8}=\frac{1}{512}$

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Example Question #4 : Expressions & Equations

Simplify:

$\displaystyle 5^5+5^5+5^5+5^5+5^5$

Possible Answers:

25^5 $\displaystyle 25^5$

5^7 $\displaystyle 5^7$

$5^{20}$ $\displaystyle 5^{20}$

5^6 $\displaystyle 5^6$

$5^{25}$ $\displaystyle 5^{25}$

Correct answer:

5^6 $\displaystyle 5^6$

Explanation:

When adding exponents, we first need to factor common terms.

Let's start by factoring out the following:

5^5 $\displaystyle 5^5$

Factor.

$\displaystyle 5^5+5^5+5^5+5^5+5^5=5^5(1+1+1+1+1)=5^5(5)=5^6$

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Example Question #212 : Exponents

Expand:

7^4 $\displaystyle 7^4$

Possible Answers:

7*7*7*7 $\displaystyle 7*7*7*7$

7*4 $\displaystyle 7*4$

$\displaystyle 4*4*4*4*4*4*4$

4*7*4*7 $\displaystyle 4*7*4*7$

$\displaystyle 7*7*7*7*7*7*7$

Correct answer:

7*7*7*7 $\displaystyle 7*7*7*7$

Explanation:

When a number is raised by an exponent, the base value is multiplied by itself the number of times that the exponential value indicates.

$\displaystyle 7^4=7*7*7*7$

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Example Question #11 : Simple Exponents

Expand:

8^5 $\displaystyle 8^5$

Possible Answers:

$\displaystyle 5*5*5*5*5*5*5*5$

5*8 $\displaystyle 5*8$

$\displaystyle 5*8*8*8*8*5$

8*5*5*8 $\displaystyle 8*5*5*8$

$\displaystyle 8*8*8*8*8$

Correct answer:

$\displaystyle 8*8*8*8*8$

Explanation:

When a number is raised by an exponent, the base value is multiplied by itself the number of times that the exponential value indicates.

$\displaystyle 8^5=8*8*8*8*8$

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Example Question #5 : Expressions & Equations

Evaluate:

2^4 $\displaystyle 2^4$

Possible Answers:

$\displaystyle 32$

$\displaystyle 6$

$\displaystyle 12$

$\displaystyle 8$

$\displaystyle 16$

Correct answer:

$\displaystyle 16$

Explanation:

When a number is raised by an exponent, the base value is multiplied by itself the number of times that the exponential value indicates.

2^4 $\displaystyle 2^4$ is expanded to 2*2*2*2 $\displaystyle 2*2*2*2$ .

The product is $\displaystyle 16$ .

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Example Question #7 : Write And Evaluate Numerical Expressions With Exponents: Ccss.Math.Content.6.Ee.A.1

Evaluate:

$4^{4}$ $\displaystyle 4^{4}$

Possible Answers:

$\displaystyle 16$

$\displaystyle 32$

256 $\displaystyle 256$

128 $\displaystyle 128$

$\displaystyle 64$

Correct answer:

256 $\displaystyle 256$

Explanation:

When a number is raised by an exponent, the base value is multiplied by itself the number of times that the exponential value indicates.

4^4 $\displaystyle 4^4$ is expanded to 4*4*4*4 $\displaystyle 4*4*4*4$ .

The product is 256 $\displaystyle 256$ .

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Example Question #1 : Expressions & Equations

Expand: 9^9 $\displaystyle 9^9$

Possible Answers:

$\displaystyle 99*99*99*99*99*99$

$\displaystyle 9*9*9*9*9*9*9*9$

9*9 $\displaystyle 9*9$

$\displaystyle 9*9*9*9*9*9*9*9*9$

$\displaystyle 9^9*9^9*9^9*9^9*9^9*9^9*9^9*9^9*9^9$

Correct answer:

$\displaystyle 9*9*9*9*9*9*9*9*9$

Explanation:

9^9 $\displaystyle 9^9$ To expand the exponent, we just multiply the base out by the exponent present.

$\displaystyle 9^9=9*9*9*9*9*9*9*9*9$

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Example Question #21 : Simple Exponents

Which of the following is the same as 4^4 $\displaystyle 4^4$ ?

Possible Answers:

16^2 $\displaystyle 16^2$

2^7 $\displaystyle 2^7$

16^1 $\displaystyle 16^1$

32^2 $\displaystyle 32^2$

8^2 $\displaystyle 8^2$

Correct answer:

16^2 $\displaystyle 16^2$

Explanation:

4^4 $\displaystyle 4^4$ is expanded out to 4*4*4*4 $\displaystyle 4*4*4*4$ . This is also the same as 16*16 $\displaystyle 16*16$ or 16^2 $\displaystyle 16^2$ which is the correct answer.

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Algebra II : Exponents

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #211 : Exponents

Example Question #682 : Mathematical Relationships And Basic Graphs

Example Question #212 : Exponents

Example Question #4 : Expressions & Equations

Example Question #212 : Exponents

Example Question #11 : Simple Exponents

Example Question #5 : Expressions & Equations

Example Question #7 : Write And Evaluate Numerical Expressions With Exponents: Ccss.Math.Content.6.Ee.A.1

Example Question #1 : Expressions & Equations

Example Question #21 : Simple Exponents

All Algebra II Resources

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