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Algebra II : Simple Exponents

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #251 : Understanding Exponents

Evaluate: $-3^0 \cdot -2^{3} \cdot -3^2$

Possible Answers:

Correct answer:

Explanation:

Use order of operations to evaluate this expression. Evaluate the exponents first.

3^0 = 1

2^3 = 8

3^2 =9

Apply the negative signs in front of these values.

$-3^0 \cdot -2^{3} \cdot -3^2 =(-1)(-8)(-9) = -72$

The answer is:

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Example Question #252 : Understanding Exponents

Evaluate: 2^2+2^5+3^0

Possible Answers:

129

128

Correct answer:

Explanation:

Rewrite the expression by expanding the exponents. A number raised to a number is multiplied by itself that many times. The exception is that any number raised to the power of zero is equal to one.

$2^2+2^5+3^0 = (2\times 2)+(2\times 2\times 2\times 2\times 2)+1$

=4+32+1=37

The answer is:

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Example Question #3391 : Algebra Ii

Expand 12^8

Possible Answers:

12^8*12^8*12^8*12^8*12^8*12^8*12^8*12^8

12*12*12*12*12*12*12*12

8*8*8*8*8*8*8*8*8*8*8*8

12*12*8*8*8*12

12*8

Correct answer:

12*12*12*12*12*12*12*12

Explanation:

To expand the exponent, we multiply the base by the power it is being raised to.

12^8=12*12*12*12*12*12*12*12

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Example Question #3392 : Algebra Ii

Expand (-6)^6

Possible Answers:

-6*6

-6*-6*-6*-6*-6*-6

6*6*6*6*6*6

-6*-6*-6*-6*-6*-6*6*6*6*6*6*6

-6^6*-6^6*-6^6*-6^6*-6^6*-6^6

Correct answer:

-6*-6*-6*-6*-6*-6

Explanation:

To expand the exponent, we multiply the base by the power it is being raised to.

(-6)^6=-6*-6*-6*-6*-6*-6

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Example Question #63 : Simple Exponents

Evaluate: $(x^{3})^3+3x^3+3x(3x^3)$

Possible Answers:

x^9+6x^4+3x^3

x^6+9x^4+3x^3

x^6+6x^4+3x^3

x^9+9x^4+3x^3

10x^3+9x^4

Correct answer:

x^9+9x^4+3x^3

Explanation:

Evaluate each term of $(x^{3})^3+3x^3+3x(3x^3)$ .

$(x^{3})^3 = (x^{3})(x^{3})(x^{3}) = x^{3+3+3} = x^9$

The term 3x^3 is already simplified.

3x(3x^3) = 9x^4

Combine all the terms. There are no like-terms.

The answer is: x^9+9x^4+3x^3

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Example Question #3393 : Algebra Ii

Convert $4^{10}$ to base .

Possible Answers:

$2^{10}$

2^8

$2^{12}$

$2^{20}$

$2^{24}$

Correct answer:

$2^{20}$

Explanation:

We know that 4=2^2 .

Therefore

$4^{10}=(2^2)^{10}=2^{20}$ .

Remember to apply the power rule of exponents.

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Example Question #264 : Understanding Exponents

Convert $2^{18}$ to base $\frac{1}{2}$ .

Possible Answers:

$(\frac{1}{2})^{18}$

$(\frac{1}{2})^{-18}$

$(\frac{1}{2})^{-36}$

$(\frac{1}{2})^{24}$

$(\frac{1}{2})^{-16}$

Correct answer:

$(\frac{1}{2})^{-18}$

Explanation:

We know that $2=\frac{1}{2}^{-1}$ .

Remember when having negative exponents

$x^{-a}=\frac{1}{x^a}$

which is the positive exponent raising base .

Therefore

$2^{18}=(\frac{1}{2}^{-1})^{18}=(\frac{1}{2})^{-18}$ .

Remember to apply the power rule of exponents.

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Example Question #265 : Understanding Exponents

Evaluate 5^6

Possible Answers:

3025

252525

125625

15625

78125

Correct answer:

15625

Explanation:

To evaluate the exponent, we expand 5^6 into 5*5*5*5*5*5 .

We just multiply the numbers out to get,

$\\ 5\times 5=25 \\25\times 5=125 \\125\times 5=625 \\625\times 5=3125 \\3125\times 5=15625$

Therefore, 5^6=15625 .

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Example Question #266 : Understanding Exponents

Evaluate -9^4

Possible Answers:

6561

729

Correct answer:

Explanation:

To evaluate the exponent, we expand -9^4 into -(9*9*9*9) .

We just multiply the numbers out to get,

$\\9\times9=81 \\81\times 9=729 \\729\times9=6561$

Remember to apply the negative sign after solving the exponent.

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Example Question #267 : Understanding Exponents

Evaluate (-8)^6

Possible Answers:

262144

164826

144262

Correct answer:

262144

Explanation:

To evaluate the exponent, we expand (-8)^6 into -8*-8*-8*-8*-8*-8 .

We just multiply the numbers out to get

$\\-8\times -8=64 \\64\times -8=-512 \\-512\times -8=4096 \\4096\times -8=-32768 \\-32768\times -8=262144$ .

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Algebra II : Simple Exponents

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #251 : Understanding Exponents

Example Question #252 : Understanding Exponents

Example Question #3391 : Algebra Ii

Example Question #3392 : Algebra Ii

Example Question #63 : Simple Exponents

Example Question #3393 : Algebra Ii

Example Question #264 : Understanding Exponents

Example Question #265 : Understanding Exponents

Example Question #266 : Understanding Exponents

Example Question #267 : Understanding Exponents

All Algebra II Resources

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