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Algebra II : Simple Exponents

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Example Questions

Example Question #735 : Mathematical Relationships And Basic Graphs

Simplify: -3^3+2^3-1^3

Possible Answers:

Correct answer:

Explanation:

Simplify each term.

$-3^3+2^3-1^3= -(3\cdot 3\cdot 3) +(2\cdot 2\cdot 2)-(1\cdot 1\cdot 1)$

The expression simplifies to:

-27+8-1 = -20

The answer is:

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Example Question #266 : Exponents

Simplify the exponents: $(\frac{1}{3})^2+(\frac{2}{5})^2$

Possible Answers:

$\frac{17}{75}$

$\frac{61}{225}$

$\frac{37}{25}$

$\frac{4}{15}$

$\frac{31}{125}$

Correct answer:

$\frac{61}{225}$

Explanation:

Simplify the terms with the exponents.

$(\frac{1}{3})^2+(\frac{2}{5})^2 = \frac{1}{9}+\frac{4}{25}$

To add the fractions, we will need a common denominator.

Multiply the two denominators together.

$25\times 9 = 225$

Convert both fractions to this denominator.

$\frac{1(25)}{9(25)}+\frac{4(9)}{25(9)} =\frac{25}{225}+\frac{36}{225}$

The numerators can be added now that the denominators are the same.

The answer is: $\frac{61}{225}$

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Example Question #271 : Exponents

Simplify: -2^6+2^3

Possible Answers:

Correct answer:

Explanation:

A number raised by a power is multiplied by itself that number of times.

Rewrite the expression.

$-2^6+2^3 = -(2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2)+(2\cdot 2\cdot 2)$

Simplify the terms.

-64+8 = -56

The answer is:

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Example Question #272 : Exponents

Simplify: -2^3+0^1+3^2+5^2

Possible Answers:

Correct answer:

Explanation:

Evaluate each term.

$-2^3 = -(2\times 2\times 2) = -8$

0^1=0

3^2=9

$5^2 = 5\times 5 = 25$

Add all the terms.

-8+9+25 = 26

The answer is:

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Example Question #273 : Exponents

Solve the exponents: 4^2+5^3-(-2)^3

Possible Answers:

133

141

149

Correct answer:

149

Explanation:

Simplify each term. An number raised to a certain integer is the number of times the number will multiply itself by.

$4^2 =4\times 4= 16$

$5^3 = 5\times 5\times 5= 125$

(-2)^3 = (-2)(-2)(-2) = -8

Determine the sum.

4^2+5^3-(-2)^3 = 16+125-(-8) = 16+125+8 = 149

The answer is: 149

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Example Question #274 : Exponents

Solve: 2^3+8^2-10^3

Possible Answers:

Correct answer:

Explanation:

Evaluate each term given.

2^3=8

8^2=64

10^3= 1000

Rewrite the expression.

2^3+8^2-10^3=8+64-1000 =-928

The answer is:

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Example Question #271 : Understanding Exponents

Evaluate: (-9)^4

Possible Answers:

7241

6561

8451

Correct answer:

6561

Explanation:

We know that (-9)^4=-9*-9*-9*-9 . The product is positive we have even number of negative signs. Therefor our answer is 6561 .

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Example Question #272 : Understanding Exponents

Evaluate: -6^3

Possible Answers:

216

Correct answer:

Explanation:

We know that -6^3 is expanded out to -(6*6*6) . Remember we apply the exponent part of PEMDAS before we add the negative sign. Therefore our answer is .

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Example Question #273 : Understanding Exponents

Expand: 6^7

Possible Answers:

7*7*7*7*7*7

6*7*6*7*6*7

6*6*6*6*6*6*6

7*6

6^7*6^7*6^7*6^7*6^7*6^7*6^7

Correct answer:

6*6*6*6*6*6*6

Explanation:

To expand the exponent, we multiply the base by whatever the exponent is.

6^7=6*6*6*6*6*6*6

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Example Question #274 : Understanding Exponents

Expand: -5^7

Possible Answers:

-(5*5*5*5*5*5*5)

-5*7

-5^7*-5^7*-5^7*-5^7*-5^7*-5^7*-5^7

-5*-5*-5*-5*-5*-5*-5

5^7*5^7*5^7*5^7*5^7*5^7*5^7

Correct answer:

-(5*5*5*5*5*5*5)

Explanation:

To expand the exponent, we multiply the base by whatever the exponent is. Because there is a negative sign present, we need to apply the exponent first and then add the negative sign.

-5^7=-(5*5*5*5*5*5*5)

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Algebra II : Simple Exponents

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #735 : Mathematical Relationships And Basic Graphs

Example Question #266 : Exponents

Example Question #271 : Exponents

Example Question #272 : Exponents

Example Question #273 : Exponents

Example Question #274 : Exponents

Example Question #271 : Understanding Exponents

Example Question #272 : Understanding Exponents

Example Question #273 : Understanding Exponents

Example Question #274 : Understanding Exponents

All Algebra II Resources

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