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Algebra II : Mathematical Relationships and Basic Graphs

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Example Questions

Example Question #431 : Exponents

Simplify:

$10^{50}\div10^{-20}$

Possible Answers:

$10^{30}$

$10^{40}$

$10^{70}$

$10^{-30}$

$10^{-100}$

Correct answer:

$10^{70}$

Explanation:

When exponents with the same base are divided, we will simply subtract the exponents and keep the base the same.

Divide:

$10^{50}\div10^{-20}=10^{50-(-20)}=10^{70}$

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Example Question #902 : Mathematical Relationships And Basic Graphs

Simplify:

$24^{-23}\div23^{-25}$

Possible Answers:

$23^{-2}$

23^4

23^2

$23^{-4}$

23^6

Correct answer:

23^2

Explanation:

When exponents with the same base are divided, we will simply subtract the exponents and keep the base the same.

Divide:

$24^{-23}\div23^{-25}=23^{-23-(-25)}=23^2$

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Example Question #102 : Multiplying And Dividing Exponents

Simplify:

36^4*6^7

Possible Answers:

$6^{36}$

$6^{15}$

$6^{38}$

$6^{56}$

$6^{28}$

Correct answer:

$6^{15}$

Explanation:

Even though we have different bases, we know that the following:

36=6^2

When an exponent is raised by another exponent, we will multiply the exponents and keep the base the same.

Simplify:

(6^2)^4=6^8

When exponents with the same base are multiplied together, we we will simply add the exponents and keep the base the same.

Multiply:

$6^8*6^7=6^{15}$

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Example Question #103 : Multiplying And Dividing Exponents

Simplify:

$4^{17}\div2^{-9}$

Possible Answers:

$2^{19}$

$2^{306}$

$2^{23}$

$2^{37}$

$2^{43}$

Correct answer:

$2^{43}$

Explanation:

Even though we have different bases, we know that the following:

4=2^2

When an exponent is raised by another exponent, we will multiply the exponents and keep the base the same.

Simplify:

$(2^2)^{17}=2^{34}$

When exponents with the same base are divided, we will simply subtract the exponents and keep the base the same.

Divide:

$2^{34}\div2^{-9}=2^{43}$

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Example Question #903 : Mathematical Relationships And Basic Graphs

Simplify the expression $\frac{x^7y^5z^9j^4}{x^9y^4z^8j^6}$ .

Possible Answers:

$x^{16}y^9z^{17}j^{10}$

$\frac{yz}{x^2j^2}$

The expression cannot be simplified.

$\frac{x^2j^2}{yz}$

$\frac{y^2z^2}{x^3j^2}$

Correct answer:

$\frac{yz}{x^2j^2}$

Explanation:

Subtract the lower number exponent from the higher. The term does in the numerator or denominator depending on which has the higher degree. The x term has degree 7 in numerator and degree 9 in denominator, so the difference (9-7) goes in the denominator.

$\frac{x^7y^5z^9j^4}{x^9y^4z^8j^6}=\frac{y^{5-4}z^{9-8}}{x^{9-7}j^{6-4}}=\frac{yz}{x^2j^2}$

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Example Question #904 : Mathematical Relationships And Basic Graphs

Simplify: $12^{8}*12^{-8}$

Possible Answers:

$12^{-64}$

$12^{16}$

$12^{24}$

$12^{-16}$

Correct answer:

Explanation:

When multiplying exponents with the same base, we just add the exponents and keep the base the same.

$12^{8}*12^{-8}=12^{8+(-8)}=12^0=1$

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Example Question #905 : Mathematical Relationships And Basic Graphs

Simplify: $10^7*10^{12}$

Possible Answers:

$10^{29}$

$10^{84}$

$10^{34}$

$10^{19}$

$10^{9}$

Correct answer:

$10^{19}$

Explanation:

When multiplying exponents with the same base, we just add the exponents and keep the base the same.

$10^7*10^{12}=10^{7+12}=10^{19}$

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Example Question #906 : Mathematical Relationships And Basic Graphs

Simplify: $13^{-14}*13^{-2}$

Possible Answers:

$13^{-28}$

$13^{46}$

$13^{-16}$

$13^{28}$

$13^{16}$

Correct answer:

$13^{-16}$

Explanation:

When multiplying exponents with the same base, we just add the exponents and keep the base the same.

$13^{-14}*13^{-2}=13^{-14+(-2)}=13^{-16}$

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Example Question #907 : Mathematical Relationships And Basic Graphs

Simplify: $15^{6}\div15^{18}$

Possible Answers:

$15^{-\frac{1}{3}}$

$15^{-3}$

$15^{\frac{1}{3}}$

$15^{-12}$

$15^{-24}$

Correct answer:

$15^{-12}$

Explanation:

When dividing exponents with the same base, we subtract the exponents and keep the base the same.

$15^{6}\div15^{18}=15^{6-18}=15^{-12}$

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Example Question #908 : Mathematical Relationships And Basic Graphs

Simplify: $12^{19}\div12^7$

Possible Answers:

$12^{4}$

$12^{12}$

$12^{26}$

$12^{-12}$

$12^{-26}$

Correct answer:

$12^{12}$

Explanation:

When dividing exponents with the same base, we subtract the exponents and keep the base the same.

$12^{19}\div12^7=12^{19-7}=12^{12}$

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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 #431 : Exponents

Example Question #902 : Mathematical Relationships And Basic Graphs

Example Question #102 : Multiplying And Dividing Exponents

Example Question #103 : Multiplying And Dividing Exponents

Example Question #903 : Mathematical Relationships And Basic Graphs

Example Question #904 : Mathematical Relationships And Basic Graphs

Example Question #905 : Mathematical Relationships And Basic Graphs

Example Question #906 : Mathematical Relationships And Basic Graphs

Example Question #907 : Mathematical Relationships And Basic Graphs

Example Question #908 : Mathematical Relationships And Basic Graphs

All Algebra II Resources

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