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Algebra II : Mathematical Relationships and Basic Graphs

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #12 : Simplifying Exponents

Simplify

$\frac{x^5y^6}{x^3y^{10}}$

Possible Answers:

$\frac{y^4}{x^2}$

x^2y^4

$x^8y^{16}$

$\frac{x^2}{y^4}$

$x^{15}y^{60}$

Correct answer:

$\frac{x^2}{y^4}$

Explanation:

When dividing variables with exponents, you subtract the denominator exponents from the numerator exponents of the corresponding variable:

$x^{5-3}y^{6-10}$ , then simplify: $x^2y^{-4}$ .

In order to remove the negative exponent, we move it to the denominator.

Therefore, the answer is $\frac{x^2}{y^4}$ .

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Example Question #21 : Simplifying Exponents

Simplify the following expression:

$\frac{x^{3}x^{-8}}{x^{7}}$

Possible Answers:

$x^{-12}$

$x^{24}$

$x^{18}$

$x^{4}$

$x^{2}$

Correct answer:

$x^{-12}$

Explanation:

When multiplying exponents, add the superscripts.

When dividing expondents, subtract the superscripts.

Thus, all you need to do here is:

3+(-8)-7=-5-7=-12 .

$\frac{x^{3}x^{-8}}{x^{7}}=x^{-12}$

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Example Question #21 : Simplifying Exponents

Solve: $\frac{z^{10}}{z^{-2}}$

Possible Answers:

$\frac{1}{z^5}$

$\frac{1}{z^{20}}$

$z^{20}$

$z^{12}$

z^8

Correct answer:

$z^{12}$

Explanation:

When dividing similar bases with an exponent, subtract the powers.

$\frac{z^{10}}{z^{-2}}= z^{(10-(-2))}= z^{12}$

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Example Question #23 : Simplifying Exponents

Simplify.

x^2*x^6

Possible Answers:

$x^{-6}$

x^3

$x^{12}$

x^8

$x^{26}$

Correct answer:

x^8

Explanation:

When multiplying exponents, we must first check to see if the factors have the same base. If they have the same bases, then we can add the exponents.

$x^2*x^6=x^{2+6}$

$x^{2+6}=x^8$

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Example Question #24 : Simplifying Exponents

Simplify.

$x^6*x^{-5}$

Possible Answers:

$x^{-1}$

$x^{11}$

$x^{-11}$

$x^{-30}$

Correct answer:

Explanation:

When multiplying exponents, we must first check to see if the factors have the same base. If they have the same bases, then we can add the exponents.

$x^6*x^{-5}=x^{6+(-5)}$

Remember that when adding a negative number to a positive number, we take the sign of the greater number and treat it as a subtraction problem. Since is greater than and is positive, our answer is positive. We will treat it as a subtraction problem.

$x^{(6-5)}=x^1$

x^1=x

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Example Question #25 : Simplifying Exponents

Simplify.

$x^9*x^{-5}*x^{-7}$

Possible Answers:

$x^{-315}$

$x^{315}$

$x^{-3}$

$x^{21}$

x^3

Correct answer:

$x^{-3}$

Explanation:

When multiplying exponents, we must first check to see if the factors have the same base. If they have the same bases, then we can add the exponents.

$x^{9}*x^{-5}*x^{-7}=x^{9+(-5)+(-7)}$

Remember that when adding a negative number to a negative number, we add the addends and place a negative sign in front of the total.

$x^{9+(-5+-7)}=x^{9+(-12)}$

Remember that when adding a negative number to a positive number, we take the sign of the greater number and treat it as a subtraction problem. Since is greater than and is negative, our answer is negative. We will treat it as a subtraction problem.

$x^{9+(-12)}=x^{-3}$

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Example Question #22 : Simplifying Exponents

Simplify.

$\frac{x^5}{x^4}$

Possible Answers:

$x^{20}$

$x^{1.25}$

x^9

$x^{-1}$

Correct answer:

Explanation:

When dividing exponents, we must first check to see if the factors have the same base. If they have the same bases, then we can subtract the exponents.

$\frac{x^5}{x^4}=x^{5-4}$

$x^{5-4}=x^{1}=x$

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Example Question #22 : Simplifying Exponents

Simplify.

$\frac{x^7}{y^3}$

Possible Answers:

(xy)^4

xy^4

$(xy)^{21}$

x^4y

$\frac{x^7}{y^3}$

Correct answer:

$\frac{x^7}{y^3}$

Explanation:

When dividing exponents, we must first check to see if the factors have the same base. If they have the same bases, then we can subtract the exponents.

These factors have different bases; therefore, we cannot simplify any further.

The answer is as follows:

$\frac{x^7}{y^3}$

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Example Question #28 : Simplifying Exponents

Simplify.

$\frac{x^8}{x^{-9}}$

Possible Answers:

$x^{17}$

x^1

x^4

$x^{-1}$

Correct answer:

$x^{17}$

Explanation:

When dividing exponents, we must first check to see if the factors have the same base. If they have the same bases, then we can subtract the exponents.

$\frac{x^8}{x^{-9}}=x^{8-(-9)}$

Remember that subtracting a negative number is the same as adding a positive number.

$x^{8-(-9)}=x^{8+9}$

$x^{8+9}=x^{17}$

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Example Question #23 : Simplifying Exponents

Simplify.

$\frac{10^{17}}{5^{17}}$

Possible Answers:

Can't be simplified.

$2^{17}$

$2^{34}$

$5^{17}$

Correct answer:

$2^{17}$

Explanation:

Although they have different bases, they do have the same exponent. We can essentially divide the base but keep the exponent constant.

$\frac{10^{17}}{5^{17}}=(\frac{10}{5})^{17}$

The answer is as follows:

$(\frac{10}{5})^{17}=2^{17}$

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Algebra II : Mathematical Relationships and Basic Graphs

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #12 : Simplifying Exponents

Example Question #21 : Simplifying Exponents

Example Question #21 : Simplifying Exponents

Example Question #23 : Simplifying Exponents

Example Question #24 : Simplifying Exponents

Example Question #25 : Simplifying Exponents

Example Question #22 : Simplifying Exponents

Example Question #22 : Simplifying Exponents

Example Question #28 : Simplifying Exponents

Example Question #23 : Simplifying Exponents

All Algebra II Resources

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