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Algebra II : Understanding Exponents

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #12 : Write And Evaluate Numerical Expressions With Exponents: Ccss.Math.Content.6.Ee.A.1

Expand:

18^8 $\displaystyle 18^8$

Possible Answers:

18*8 $\displaystyle 18*8$

$\displaystyle 18*18*18*18*18*18*18*18$

$\displaystyle 18*18*18*18*8*8*8*8$

$\displaystyle 18*8*8*18$

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

Correct answer:

$\displaystyle 18*18*18*18*18*18*18*18$

Explanation:

When expanding an exponent, we must multiply the base by itself for the number of indicated by the exponential value.

$\displaystyle 18^8=18*18*18*18*18*18*18*18$

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Example Question #241 : Understanding Exponents

Evaluate:

15^3 $\displaystyle 15^3$

Possible Answers:

2575 $\displaystyle 2575$

3375 $\displaystyle 3375$

1515 $\displaystyle 1515$

2525 $\displaystyle 2525$

1025 $\displaystyle 1025$

Correct answer:

3375 $\displaystyle 3375$

Explanation:

When expanding an exponent, we must multiply the base by itself for the number of indicated by the exponential value.

15^3 $\displaystyle 15^3$ is expanded out to the following:

$\displaystyle 15*15*15$

The product is 3375 $\displaystyle 3375$.

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Example Question #243 : Understanding Exponents

Convert $8^{12}$ $\displaystyle 8^{12}$ to base $\displaystyle 4$.

Possible Answers:

$4^{16}$ $\displaystyle 4^{16}$

$4^{18}$ $\displaystyle 4^{18}$

$4^{20}$ $\displaystyle 4^{20}$

$4^{12}$ $\displaystyle 4^{12}$

$4^{24}$ $\displaystyle 4^{24}$

Correct answer:

$4^{18}$ $\displaystyle 4^{18}$

Explanation:

First, we know that 8=2^3 $\displaystyle 8=2^3$.

Apply the power rule of exponents:

$\displaystyle (a^m)^n=a^m^n$

We can then write the following expression:

$(2^3)^{12}=2^{36}$ $\displaystyle (2^3)^{12}=2^{36}$

Second, we know that 4=2^2 $\displaystyle 4=2^2$.

By applying the same rule, we will get the following expression:

$(2^2)^x=2^{36}$ $\displaystyle (2^2)^x=2^{36}$

Therefore:

2x=36 $\displaystyle 2x=36$ and x=18 $\displaystyle x=18$

The answer is $4^{18}$ $\displaystyle 4^{18}$.

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Example Question #712 : Mathematical Relationships And Basic Graphs

Change 27^6 $\displaystyle 27^6$ to base $\displaystyle 3$.

Possible Answers:

$3^{27}$ $\displaystyle 3^{27}$

$3^{9}$ $\displaystyle 3^{9}$

$3^{18}$ $\displaystyle 3^{18}$

$3^{12}$ $\displaystyle 3^{12}$

$3^{15}$ $\displaystyle 3^{15}$

Correct answer:

$3^{18}$ $\displaystyle 3^{18}$

Explanation:

First, we know that 27=3^3 $\displaystyle 27=3^3$.

Apply the power rule of exponents:

$\displaystyle (a^m)^n=a^m^n$

We can then write the following expression:

(3^3)^6 $\displaystyle (3^3)^6$ or $3^{18}$ $\displaystyle 3^{18}$

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Example Question #3371 : Algebra Ii

Convert $8^{12}$ $\displaystyle 8^{12}$ to base $\displaystyle 2$.

Possible Answers:

$2^{36}$ $\displaystyle 2^{36}$

$2^{18}$ $\displaystyle 2^{18}$

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

$2^{60}$ $\displaystyle 2^{60}$

$2^{40}$ $\displaystyle 2^{40}$

Correct answer:

$2^{36}$ $\displaystyle 2^{36}$

Explanation:

First, we know that 8=2^3 $\displaystyle 8=2^3$.

Apply the power rule of exponents:

$\displaystyle (a^m)^n=a^m^n$

We can then write the following expression:

$(2^3)^{12}=2^{36}$ $\displaystyle (2^3)^{12}=2^{36}$

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Example Question #244 : Understanding Exponents

Convert 16^9 $\displaystyle 16^9$ to base $\displaystyle 8$.

Possible Answers:

8^9 $\displaystyle 8^9$

$8^{13}$ $\displaystyle 8^{13}$

$8^{16}$ $\displaystyle 8^{16}$

$8^{12}$ $\displaystyle 8^{12}$

$8^{24}$ $\displaystyle 8^{24}$

Correct answer:

$8^{12}$ $\displaystyle 8^{12}$

Explanation:

First, we know that 16=2^4 $\displaystyle 16=2^4$.

Apply the power rule of exponents:

$\displaystyle (a^m)^n=a^m^n$

We can then write the following expression:

$(2^4)^{9}=2^{36}$ $\displaystyle (2^4)^{9}=2^{36}$

Second, we know that 8=2^3 $\displaystyle 8=2^3$.

By applying the same rule, we will get the following expression:

$(2^3)^x=2^{36}$ $\displaystyle (2^3)^x=2^{36}$

Therefore:

3x=36 $\displaystyle 3x=36$

Simplify and solve for $\displaystyle x$.

x=12 $\displaystyle x=12$

The answer is $8^{12}$ $\displaystyle 8^{12}$.

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Example Question #242 : Understanding Exponents

Expand 11^4 $\displaystyle 11^4$

Possible Answers:

$\displaystyle 11^4*11^4*11^4*11^4$

11*4 $\displaystyle 11*4$

$\displaystyle 4*4*4*11*11*11$

$\displaystyle 11*11*11*11$

$\displaystyle 4*4*4*4*4*4*4*4*4*4*4$

Correct answer:

$\displaystyle 11*11*11*11$

Explanation:

When expanding exponents, we repeat the base by the exponential value.

$\displaystyle 11^4=11*11*11*11$

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Example Question #243 : Understanding Exponents

Expand 2^7 $\displaystyle 2^7$

Possible Answers:

$\displaystyle 2*2*2*2*2*2*2$

$\displaystyle 2^7*2^7*2^7*2^7*2^7*2^7*2^7$

2*7 $\displaystyle 2*7$

7*7 $\displaystyle 7*7$

2*2*7*7 $\displaystyle 2*2*7*7$

Correct answer:

$\displaystyle 2*2*2*2*2*2*2$

Explanation:

When expanding exponents, we repeat the base by the exponential value.

2^7= $\displaystyle 2^7=$$\displaystyle 2*2*2*2*2*2*2$

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Example Question #246 : Understanding Exponents

Expand $\frac{1}{2}^8$ $\displaystyle \frac{1}{2}^8$

Possible Answers:

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

$\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}$ $\displaystyle \frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}$

$\frac{1}{2}^8*8$ $\displaystyle \frac{1}{2}^8*8$

$\frac{1}{2}*\frac{1}{2}*8*8$ $\displaystyle \frac{1}{2}*\frac{1}{2}*8*8$

$\frac{1}{2}^8*\frac{1}{2}^8*\frac{1}{2}^8*\frac{1}{2}^8*\frac{1}{2}^8*\frac{1}{2}^8*\frac{1}{2}^8*\frac{1}{2}^8$ $\displaystyle \frac{1}{2}^8*\frac{1}{2}^8*\frac{1}{2}^8*\frac{1}{2}^8*\frac{1}{2}^8*\frac{1}{2}^8*\frac{1}{2}^8*\frac{1}{2}^8$

Correct answer:

Explanation:

When expanding exponents, we repeat the base by the exponential value.

$\frac{1}{2}^8=\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}$ $\displaystyle \frac{1}{2}^8=\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}$

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Example Question #244 : Understanding Exponents

Expand (-4)^3 $\displaystyle (-4)^3$

Possible Answers:

-4*3 $\displaystyle -4*3$

3*3*3*3 $\displaystyle 3*3*3*3$

$\displaystyle (-4)^3*(-4)^3*(-4)^3$

$\displaystyle -4*-4*-4$

4*4*4 $\displaystyle 4*4*4$

Correct answer:

$\displaystyle -4*-4*-4$

Explanation:

When expanding exponents, we repeat the base by the exponential value.

$\displaystyle (-4)^3=-4*-4*-4$

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Algebra II : Understanding Exponents

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #12 : Write And Evaluate Numerical Expressions With Exponents: Ccss.Math.Content.6.Ee.A.1

Example Question #241 : Understanding Exponents

Example Question #243 : Understanding Exponents

Example Question #712 : Mathematical Relationships And Basic Graphs

Example Question #3371 : Algebra Ii

Example Question #244 : Understanding Exponents

Example Question #242 : Understanding Exponents

Example Question #243 : Understanding Exponents

Example Question #246 : Understanding Exponents

Example Question #244 : Understanding Exponents

All Algebra II Resources

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