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Algebra II : Understanding Exponents

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #21 : Simple Exponents

Evaluate $\frac{1}{2}^3$

Possible Answers:

$\frac{1}{6}$

$\frac{1}{16}$

$\frac{1}{8}$

$\frac{1}{4}$

$\frac{3}{8}$

Correct answer:

$\frac{1}{8}$

Explanation:

We can expand $\frac{1}{2}^3$ to $\frac{1}{2}*\frac{1}{2}*\frac{1}{2}$ . The product of these fractions is $\frac{1}{8}$ .

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Example Question #23 : Simple Exponents

Simplify: 2^5*4^6

Possible Answers:

$8^{11}$

4^7

$2^{15}$

$2^{17}$

$4^{8}$

Correct answer:

$2^{17}$

Explanation:

Although the exponents are not the same base, we can change the bases. Let's change base to base . We know 4=2^2 . By applying power rule of exponents, we get $4^6=(2^2)^6=2^{12}$ . Finally, with the same base, we just add the exponents and keep the base the same.

$2^5*2^{12}=2^{5+12}=2^{17}$

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Example Question #22 : Simple Exponents

Evaluate (-3)^4

Possible Answers:

Correct answer:

Explanation:

With the negative inside the parenthesis, we multiply the base four times. Since the exponent is even, our answer will be even. Answer is .

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Example Question #8 : Expressions & Equations

Expand: 10^7

Possible Answers:

7*7*7*7*7*7*7*7*7*7

10*10*10*10*10

10*10*10*10*10*10*10

10*7

7*10*7*10

Correct answer:

10*10*10*10*10*10*10

Explanation:

To expand the exponent, we just multiply the base out by the exponent present.

10^7= 10*10*10*10*10*10*10

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Example Question #25 : Simple Exponents

Which exponent is NOT the same as 3^6

Possible Answers:

9^3

243*3

27^2

27^3

729

Correct answer:

27^3

Explanation:

We can express 3^6 as 3*3*3*3*3*3 which is the same as 9*9*9 . That is also 9^3 . We can also say it is 27^2 or 729 . Lastly, if we multiply by itself times, we get 243 and another leftover to be multiplied. This leaves 27^3 as the correct answer.

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Example Question #223 : Understanding Exponents

Evaluate $\left (\frac{2}{3} \right )^4$

Possible Answers:

$\frac{3}{2}$

$\frac{16}{81}$

$\frac{81}{16}$

$\frac{2}{3}$

$\frac{24}{35}$

Correct answer:

$\frac{16}{81}$

Explanation:

We can expand $\left (\frac{2}{3} \right )^4$ to $\frac{2}{3}*\frac{2}{3}*\frac{2}{3}*\frac{2}{3}$ . The product is $\frac{16}{81}$ .

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Example Question #27 : Simple Exponents

Convert $2^{12}$ to base .

Possible Answers:

8^9

8^3

8^4

8^5

8^6

Correct answer:

8^4

Explanation:

We know 8=2^3 . Now, we need to know the exponent that raises base to match our question. We set-up as such: $(2^3)^x=2^{12}$ .

3x=12 Divide on both sides.

x=4 Answer is 8^4

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Example Question #23 : Simple Exponents

Evaluate: -2^6

Possible Answers:

Correct answer:

Explanation:

-2^6 We need to remember to do the exponent first before applying the negative sign.

Answer is .

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Example Question #31 : Simple Exponents

Expand:

12^4

Possible Answers:

12*12*12*12

12*12*12*12*4*4*4*4

12*4

144*16

4*4*4*4*4*4*4*4*4*4*4*4

Correct answer:

12*12*12*12

Explanation:

When expanding exponents, we simply multiply the base by itself for the number of times indicated by the exponential value.

12^4=12*12*12*12

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Example Question #12 : Expressions & Equations

Evaluate:

7^4

Possible Answers:

4949

2401

4703

2603

7777

Correct answer:

2401

Explanation:

When expanding exponents, we simply multiply the base by itself for the number of times indicated by the exponential value.

7^4 is expanded out to 7*7*7*7 .

When we multiply the numbers, we get a product of 2401 .

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Algebra II : Understanding Exponents

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #21 : Simple Exponents

Example Question #23 : Simple Exponents

Example Question #22 : Simple Exponents

Example Question #8 : Expressions & Equations

Example Question #25 : Simple Exponents

Example Question #223 : Understanding Exponents

Example Question #27 : Simple Exponents

Example Question #23 : Simple Exponents

Example Question #31 : Simple Exponents

Example Question #12 : Expressions & Equations

All Algebra II Resources

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