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Algebra II : Understanding Exponents

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #291 : Understanding Exponents

Solve: $(-\frac{2}{5})^3+2(2^{0})$

Possible Answers:

$\frac{8}{5}$

$-\frac{4}{125}$

$-\frac{8}{125}$

$\frac{242}{125}$

$\frac{81}{5}$

Correct answer:

$\frac{242}{125}$

Explanation:

Evaluate each term.

$(-\frac{2}{5})^3 = (-\frac{2}{5})(-\frac{2}{5})(-\frac{2}{5}) = -\frac{8}{125}$

The value of any number to the zeroth power is equal to one.

$2(2^{0}) = 2(1)=2$

Add the two terms.

$-\frac{8}{125}+2 = -\frac{8}{125}+\frac{250}{125} =\frac{242}{125}$

This term is irreducible.

The answer is: $\frac{242}{125}$

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Example Question #292 : Understanding Exponents

Simplify: $(2^3\times 2^{-1})^2$

Possible Answers:

$\frac{1}{16}$

$\frac{1}{8}$

Correct answer:

Explanation:

Simplify the terms inside the parentheses first. Since both terms have the similar base, the exponents can be added.

$(2^3\times 2^{-1})^2=(2^{3+(-1)})^2 = (2^2)^2 = 2^4$

Simplify this term.

$2^4=2\times2\times 2\times2$

The answer is:

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Example Question #293 : Understanding Exponents

Simplify: 3^3+4^2-0^3

Possible Answers:

Correct answer:

Explanation:

Evaluate each term given.

3^3 = (3)(3)(3) = 27

4^2 = (4)(4)=16

0^3 = (0) (0) (0) = 0

Rewrite the terms.

27+16-0 =43

The answer is:

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Example Question #294 : Understanding Exponents

Solve: -4^3+(-2)^4-1^5

Possible Answers:

Correct answer:

Explanation:

Evaluate each term.

4^3 = (4)(4)(4) = 64

(-2)^4 =(-2)(-2)(-2)(-2)= 16

1^5 = (1)(1)(1)(1)(1) = 1

Replace the values.

-4^3+(-2)^4-1^5 = -64 +16-1=-49

The answer is:

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Example Question #295 : Understanding Exponents

Simplify: -2^5-3^4-4^3+5^2

Possible Answers:

138

$\textup{The answer is not given.}$

Correct answer:

Explanation:

Evaluate each term. The powers indicate how many times the integer is multiplied by itself.

2^5 = (2) (2) (2) (2) (2)= 32

3^4 = (3)(3)(3)(3) = 81

4^3 = (4)(4)(4)= 64

5^2 = (5)(5) = 25

Replace all values.

-32-81-64+25=-152

The answer is:

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Example Question #296 : Understanding Exponents

Solve: 3^0+(-1)^0+0^0

Possible Answers:

$\textup{Undefined.}$

Correct answer:

$\textup{Undefined.}$

Explanation:

Evaluate each term.

3^0 = 1

(-1)^0 = 1

$0^0 = \textup{Indeterminate}$

Any value to the power of zero, except zero is defined.

The answer is: $\textup{Undefined.}$

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Example Question #297 : Understanding Exponents

Solve: $(\frac{2}{3})^3+(\frac{1}{3})^2$

Possible Answers:

$\frac{13}{27}$

$\frac{1}{3}$

$\frac{9}{2}$

$\frac{9}{11}$

$\frac{11}{27}$

Correct answer:

$\frac{11}{27}$

Explanation:

Solve each fraction by expanding the terms.

$(\frac{2}{3})^3=(\frac{2}{3})(\frac{2}{3})(\frac{2}{3}) = \frac{8}{27}$

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

Add the fractions. Change the fraction one ninth to a common fraction with the first fraction.

$\frac{8}{27}+\frac{1}{9} = \frac{8}{27}+\frac{3}{27} = \frac{11}{27}$

The answer is: $\frac{11}{27}$

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Example Question #91 : Simple Exponents

Solve: 2^3+3(2)^3+10(2)^3

Possible Answers:

110

$\textup{The answer is not given.}$

112

Correct answer:

112

Explanation:

Notice that the values of each term shares the quantity (2^3) .

This means that this is a like-term of all the terms, and the coefficients can be added.

2^3+3(2)^3+10(2)^3 = 1(2^3)+3(2)^3+10(2)^3 =14(2^3)

Reduce the cube.

= 14(8) = 112

The answer is: 112

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Example Question #298 : Understanding Exponents

Simplify: (-2)^3-2^3+4^2

Possible Answers:

Correct answer:

Explanation:

Simplify each term.

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

2^3 =8

4^2=16

Replace all the final values.

(-2)^3-2^3+4^2 = -8-8+16 = 0

The answer is:

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Example Question #101 : Simple Exponents

Try without a calculator:

Which is true about $0^{0}$ ?

Possible Answers:

$0^{0} = 1$

$0^{0} = 0$

$0^{0}$ is an undefined quantity.

$0^{0}=2$

Cannot be determined

Correct answer:

$0^{0}$ is an undefined quantity.

Explanation:

$0^{0}$ is considered to be an expression of undefined value.

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Algebra II : Understanding Exponents

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #291 : Understanding Exponents

Example Question #292 : Understanding Exponents

Example Question #293 : Understanding Exponents

Example Question #294 : Understanding Exponents

Example Question #295 : Understanding Exponents

Example Question #296 : Understanding Exponents

Example Question #297 : Understanding Exponents

Example Question #91 : Simple Exponents

Example Question #298 : Understanding Exponents

Example Question #101 : Simple Exponents

All Algebra II Resources

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