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Algebra II : Algebra II

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Example Questions

Example Question #255 : Understanding Exponents

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

Possible Answers:

$\displaystyle 54$

$\displaystyle 72$

$\displaystyle -72$

$\displaystyle 0$

$\displaystyle -54$

Correct answer:

$\displaystyle -72$

Explanation:

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

3^0 = 1 $\displaystyle 3^0 = 1$

2^3 = 8 $\displaystyle 2^3 = 8$

3^2 =9 $\displaystyle 3^2 =9$

Apply the negative signs in front of these values.

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

The answer is: $\displaystyle -72$

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Example Question #252 : Understanding Exponents

Evaluate: $\displaystyle 2^2+2^5+3^0$

Possible Answers:

$\displaystyle 15$

$\displaystyle 37$

129 $\displaystyle 129$

128 $\displaystyle 128$

$\displaystyle 36$

Correct answer:

$\displaystyle 37$

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.

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

$\displaystyle =4+32+1=37$

The answer is: $\displaystyle 37$

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Example Question #3391 : Algebra Ii

Expand 12^8 $\displaystyle 12^8$

Possible Answers:

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

$\displaystyle 12*12*8*8*8*12$

$\displaystyle 12*12*12*12*12*12*12*12$

12*8 $\displaystyle 12*8$

$\displaystyle 12^8*12^8*12^8*12^8*12^8*12^8*12^8*12^8$

Correct answer:

$\displaystyle 12*12*12*12*12*12*12*12$

Explanation:

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

$\displaystyle 12^8=12*12*12*12*12*12*12*12$

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Example Question #3392 : Algebra Ii

Expand (-6)^6 $\displaystyle (-6)^6$

Possible Answers:

-6*6 $\displaystyle -6*6$

$\displaystyle 6*6*6*6*6*6$

$\displaystyle -6^6*-6^6*-6^6*-6^6*-6^6*-6^6$

$\displaystyle -6*-6*-6*-6*-6*-6$

$\displaystyle -6*-6*-6*-6*-6*-6*6*6*6*6*6*6$

Correct answer:

$\displaystyle -6*-6*-6*-6*-6*-6$

Explanation:

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

$\displaystyle (-6)^6=-6*-6*-6*-6*-6*-6$

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Example Question #263 : Exponents

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

Possible Answers:

$\displaystyle 10x^3+9x^4$

$\displaystyle x^9+6x^4+3x^3$

$\displaystyle x^6+9x^4+3x^3$

$\displaystyle x^6+6x^4+3x^3$

$\displaystyle x^9+9x^4+3x^3$

Correct answer:

$\displaystyle x^9+9x^4+3x^3$

Explanation:

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

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

The term 3x^3 $\displaystyle 3x^3$ is already simplified.

$\displaystyle 3x(3x^3) = 9x^4$

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

The answer is: $\displaystyle x^9+9x^4+3x^3$

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Example Question #3393 : Algebra Ii

Convert $4^{10}$ $\displaystyle 4^{10}$ to base $\displaystyle 2$.

Possible Answers:

$2^{24}$ $\displaystyle 2^{24}$

$2^{10}$ $\displaystyle 2^{10}$

$2^{20}$ $\displaystyle 2^{20}$

2^8 $\displaystyle 2^8$

$2^{12}$ $\displaystyle 2^{12}$

Correct answer:

$2^{20}$ $\displaystyle 2^{20}$

Explanation:

We know that 4=2^2 $\displaystyle 4=2^2$.

Therefore

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

Remember to apply the power rule of exponents.

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Example Question #265 : Exponents

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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

Remember when having negative exponents

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

which $\displaystyle a$ is the positive exponent raising base $\displaystyle x$.

Therefore

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

Remember to apply the power rule of exponents.

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Example Question #64 : Simple Exponents

Evaluate 5^6 $\displaystyle 5^6$

Possible Answers:

252525 $\displaystyle 252525$

15625 $\displaystyle 15625$

78125 $\displaystyle 78125$

125625 $\displaystyle 125625$

3025 $\displaystyle 3025$

Correct answer:

15625 $\displaystyle 15625$

Explanation:

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

We just multiply the numbers out to get,

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

Therefore, $\displaystyle 5^6=15625$.

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Example Question #266 : Exponents

Evaluate -9^4 $\displaystyle -9^4$

Possible Answers:

729 $\displaystyle 729$

6561 $\displaystyle 6561$

$\displaystyle -6561$

$\displaystyle -729$

$\displaystyle -59049$

Correct answer:

$\displaystyle -6561$

Explanation:

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

We just multiply the numbers out to get,

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

Remember to apply the negative sign after solving the exponent.

$\displaystyle -6561$

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Example Question #267 : Exponents

Evaluate (-8)^6 $\displaystyle (-8)^6$

Possible Answers:

262144 $\displaystyle 262144$

144262 $\displaystyle 144262$

$\displaystyle -144262$

$\displaystyle -262144$

164826 $\displaystyle 164826$

Correct answer:

262144 $\displaystyle 262144$

Explanation:

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

We just multiply the numbers out to get

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

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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #255 : Understanding Exponents

Example Question #252 : Understanding Exponents

Example Question #3391 : Algebra Ii

Example Question #3392 : Algebra Ii

Example Question #263 : Exponents

Example Question #3393 : Algebra Ii

Example Question #265 : Exponents

Example Question #64 : Simple Exponents

Example Question #266 : Exponents

Example Question #267 : Exponents

All Algebra II Resources

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