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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 #60 : Multiplying And Dividing Exponents

Simplify $\frac{x^{3}\cdot x^{5}\cdot x}{x^{2}}$

Possible Answers:

$\frac{x^{15}}{x^{2}}$

$x^{7}$

$x^{13}$

$x^{9}$

$x^{11}$

Correct answer:

$x^{7}$

Explanation:

When multiplying the same variables or numbers with exponents, the exponents add. When dividing the same variables or numbers, the exponent(s) in the denominator are subtracted from those in the numerator.

$\frac{x^{3}\cdot x^{5}\cdot x}{x^{2}}$

$\frac{x^{3+5+1}}{x^{2}}$

$\frac{x^{9}}{x^{2}}$

$x^{9-2}$

$x^{7}$

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Example Question #61 : Simplifying Exponents

Simplify $\frac{4x^{2}y^{2}z^{3}}{12xy^{5}z}$

Possible Answers:

$\frac{xz^{2}}{3y^{3}}$

$\frac{x^{3}y^{3}z^{4}}{3}$

$\frac{z^{2}x^{2}}{3y^{8}}$

$3xz^{2}y^{3}$

$\frac{4xz^{2}}{12y^{3}}$

Correct answer:

$\frac{xz^{2}}{3y^{3}}$

Explanation:

Numbers in the numerator and denominator can be simplified by dividing them by the same number. Variables in the numerator and denominator cancel each other out, which can be done by subtracting the exponents in the denominator from the exponents on the same variable in the numerator.

$\frac{4x^{2}y^{2}z^{3}}{12xy^{5}z}$

First, reduce the 4 and 12 by dividing each of them by 4

$\frac{x^{2}y^{2}z^{3}}{3xy^{5}z}$

Now simplify the variables, remembering that a variable without an exponent is to the power of 1

$\frac{x^{2-1}y^{2-5}z^{3-1}}{3}$

$\frac{xy^{-3}z^{2}}{3}$

Now, make any negative exponents positive by putting them on the other part of the fraction, which is the same as taking the reciprocal.

$\frac{xz^{2}}{3y^{3}}$

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Example Question #391 : Exponents

Simplify:

$\frac{6^{12}}{6^{18}}$

Possible Answers:

$6^{\frac{2}{3}}$

$6^{-6}$

$-6^{6}$

$6^{15}$

$6^{30}$

Correct answer:

$6^{-6}$

Explanation:

When dividing exponents with the same base, we just subtract the exponents.

$\frac{6^{12}}{6^{18}}=6^{12-18}=6^{-6}$

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Example Question #3522 : Algebra Ii

Simplify:

$\frac{2^{50}*3^{14}}{2^{48}*3^{16}}$

Possible Answers:

$\frac{1}{4}$

$\frac{1}{36}$

$\frac{1}{9}$

$\frac{4}{9}$

Correct answer:

$\frac{4}{9}$

Explanation:

When dividing exponents with the same base, we just subtract the exponents.

$\frac{2^{50}*3^{14}}{2^{48}*3^{16}}=2^{50-48}*3^{14-16}=2^2*3^{-2}$

An exponent that is negative is just $x^{-a}=\frac{1}{x^a}$ where is just the positive number and is the base. Let's evaluate.

$2^2*3^{-2}=4*\frac{1}{9}=\frac{4}{9}$

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Example Question #3523 : Algebra Ii

Simplify:

$\frac{6^{48}}{2^{24}*3^{24}}$

Possible Answers:

$6^{-528}$

$2^{-24}*3^{-24}$

$2^{24}*3^{24}$

$6^{24}$

Correct answer:

$6^{24}$

Explanation:

Although we have different bases, we can still convert the bases of the denominator to the base of the numerator as long as our exponents are the same. When that happens, we just multiply the bases and keep the exponent.

$\frac{6^{48}}{2^{24}*3^{24}}=\frac{6^{48}}{6^{24}}$ When dividing exponents with the same base, we just subtract the exponents.

$\frac{6^{48}}{6^{24}}=6^{48-24}=6^{24}$

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Example Question #392 : Exponents

Simplify:

$4^{23}*4^{19}$

Possible Answers:

$4^{94}$

$4^{437}$

$4^{42}$

$16^{42}$

$16^{437}$

Correct answer:

$4^{42}$

Explanation:

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

$4^{23}*4^{19}=4^{23+19}=4^{42}$

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Example Question #393 : Exponents

Simplify:

8^7*4^7

Possible Answers:

$32^{14}$

$8^{49}$

32^7

$8^{8}$

$32^{49}$

Correct answer:

32^7

Explanation:

When multiplying exponents that are the same but with different bases, we just multiply the bases and keep the exponents the same.

8^7*4^7=32^7

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Example Question #3526 : Algebra Ii

Simplify:

5^4*25^3

Possible Answers:

$5^{10}$

$5^{24}$

$25^{12}$

$5^{12}$

25^4

Correct answer:

$5^{10}$

Explanation:

Although we have different exponents and bases, we can convert them to the same bases. In this case, we will do a base of . We know 25=5^2 . That means 25^3=(5^2)^3=5^6 . Remember when exponents are being raised by another exponent, we just multiply the powers. Now, we can just add the exponents.

$5^4*5^6=5^{10}$

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Example Question #394 : Exponents

Evaluate:

15^7*15^8

Possible Answers:

$15^{56}$

$225^{56}$

$15^{15}$

$30^{15}$

$225^{15}$

Correct answer:

$15^{15}$

Explanation:

When multiplying with same base but different exponents, you just add the exponents and keep the base the same.

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

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Example Question #395 : Exponents

Evaluate:

$12^{-4}*12^{5}$

Possible Answers:

$\frac{1}{20}$

$12^{-20}$

$\frac{1}{144}$

144

Correct answer:

Explanation:

When multiplying with same base but different exponents, you just add the exponents and keep the base the same.

$12^{-4}*12^{5}=12^{-4+5}=12^{1}=12$

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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 #60 : Multiplying And Dividing Exponents

Example Question #61 : Simplifying Exponents

Example Question #391 : Exponents

Example Question #3522 : Algebra Ii

Example Question #3523 : Algebra Ii

Example Question #392 : Exponents

Example Question #393 : Exponents

Example Question #3526 : Algebra Ii

Example Question #394 : Exponents

Example Question #395 : Exponents

All Algebra II Resources

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