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Algebra II : Mathematical Relationships and Basic Graphs

Study concepts, example questions & explanations for Algebra II

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10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #88 : Simplifying Exponents

Simplify: $6^{88}\div6^{44}$

Possible Answers:

$6^{44}$

$6^{22}$

$6^{48}$

$6^{11}$

6^2

Correct answer:

$6^{44}$

Explanation:

When dividing exponents with the same base, we subtract the exponents while keeping the base the same.

$6^{88}\div6^{44}=6^{88-44}=6^{44}$

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Example Question #3553 : Algebra Ii

Simplify: $19^{18}\div19^{24}$

Possible Answers:

$19^{-4}$

$19^{4}$

$19^{-6}$

$19^{-8}$

$19^{3}$

Correct answer:

$19^{-6}$

Explanation:

When dividing exponents with the same base, we subtract the exponents while keeping the base the same.

$19^{18}\div19^{24}=19^{18-24}=19^{-6}$

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Example Question #3554 : Algebra Ii

Simplify: $20^{12}\div20^{-3}$

Possible Answers:

$20^{15}$

20^8

$20^{-4}$

$20^{-9}$

20^9

Correct answer:

$20^{15}$

Explanation:

When dividing exponents with the same base, we subtract the exponents while keeping the base the same.

$20^{12}\div20^{-3}=20^{12-(-3)}=20^{15}$

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Example Question #3556 : Algebra Ii

Simplify: $2^{18}*4^6$

Possible Answers:

$4^{36}$

$8^{24}$

$2^{24}$

$2^{30}$

$8^{108}$

Correct answer:

$2^{30}$

Explanation:

Although the bases are not the same, we know that 4=2^2 . Therefore, $4^6=(2^2)^6=2^{12}$ . When multiplying exponents with the same base, we just add the exponents and keep the base the same.

$2^{18}*2^{12}=2^{18+12}=2^{30}$

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Example Question #94 : Multiplying And Dividing Exponents

Simplify: $27^7\div3^9$

Possible Answers:

$3^{18}$

3^4

3^6

$3^{12}$

Correct answer:

$3^{12}$

Explanation:

Although the base is not the same, we know that 27=3^3 . Therefore $27^7=(3^3)^7=3^{21}$ . When dividing exponents with the same base, we subtract the exponents while keeping the base the same.

$3^{21}\div3^9=3^{21-9}=3^{12}$

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Example Question #95 : Multiplying And Dividing Exponents

Simplify:

$\frac{p^7q^4}{p^{-2}q^6}\cdot (p^2q^2)^{-1}$

Possible Answers:

p^7

p^9q^4

$\frac{q^4}{p^7}$

$\frac{p^7}{q^4}$

Correct answer:

$\frac{p^7}{q^4}$

Explanation:

To simplify, we can subtract the numerator and denominator exponents from like terms, with negative exponents in the denominator adding to those in the numerator, and positive ones in the numerator subtracting from those in the denominator:

$\frac{p^9}{q^2}\cdot (p^2q^2)^{-1}$

Next, we can distribute the negative exponent to the terms inside the parentheses (property of exponents):

$\frac{p^9}{q^2}\cdot (p^{-2}q^{-2})$

Finally, add the exponents of the like base terms (property of exponents), because everything is multiplied together, but keep in mind that the q term is in the denominator (so its exponent is negative when in the numerator):

$p^7\cdot q^{-4}=\frac{p^7}{q^4}$

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Example Question #3555 : Algebra Ii

Simplify:

$9^9\div9^{12}$

Possible Answers:

9^3

$9^{21}$

$9^{-21}$

$9^{12}$

$9^{-3}$

Correct answer:

$9^{-3}$

Explanation:

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

Divide:

$9^9\div9^{12}=9^{9-12}=9^{-3}$

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Example Question #3556 : Algebra Ii

Simplify:

8^8*8^8

Possible Answers:

$8^{64}$

$64^{64}$

64^8

$8^{16}$

$64^{16}$

Correct answer:

$8^{16}$

Explanation:

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

Multiply:

$8^8*8^8=8^{8+8}=8^{16}$

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Example Question #421 : Exponents

Simplify:

$17^5*17^{-6}$

Possible Answers:

$17^{-1}$

$17^{-30}$

$17^{30}$

$17^{-11}$

Correct answer:

$17^{-1}$

Explanation:

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

Multiply:

$17^5*17^{-6}=17^{5+(-6)}=17^{-1}$

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Example Question #422 : Exponents

Simplify:

$18^{-3}*18^{-4}$

Possible Answers:

$18^{-12}$

$18^{-7}$

$18^{12}$

$18^{-1}$

Correct answer:

$18^{-7}$

Explanation:

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

Multiply:

$18^{-3}*18^{-4}=18^{-3+(-4)}=18^{-7}$

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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 #88 : Simplifying Exponents

Example Question #3553 : Algebra Ii

Example Question #3554 : Algebra Ii

Example Question #3556 : Algebra Ii

Example Question #94 : Multiplying And Dividing Exponents

Example Question #95 : Multiplying And Dividing Exponents

Example Question #3555 : Algebra Ii

Example Question #3556 : Algebra Ii

Example Question #421 : Exponents

Example Question #422 : Exponents

All Algebra II Resources

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