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Algebra II : Multiplying and Dividing Exponents

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Example Questions

Example Question #81 : Simplifying Exponents

Simplify: $4^7*4^{12}$ $\displaystyle 4^7*4^{12}$

Possible Answers:

$4^{84}$ $\displaystyle 4^{84}$

$4^{28}$ $\displaystyle 4^{28}$

$4^{36}$ $\displaystyle 4^{36}$

$4^{19}$ $\displaystyle 4^{19}$

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

Correct answer:

$4^{19}$ $\displaystyle 4^{19}$

Explanation:

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

$4^{7}*4^{12}=4^{7+12}=4^{19}$ $\displaystyle 4^{7}*4^{12}=4^{7+12}=4^{19}$

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Example Question #82 : Simplifying Exponents

Simplify: $5^{17}*5^{23}$ $\displaystyle 5^{17}*5^{23}$

Possible Answers:

$5^{40}$ $\displaystyle 5^{40}$

$5^{50}$ $\displaystyle 5^{50}$

$5^{42}$ $\displaystyle 5^{42}$

$5^{235}$ $\displaystyle 5^{235}$

$5^{391}$ $\displaystyle 5^{391}$

Correct answer:

$5^{40}$ $\displaystyle 5^{40}$

Explanation:

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

$5^{17}*5^{23}=5^{17+23}=5^{40}$ $\displaystyle 5^{17}*5^{23}=5^{17+23}=5^{40}$

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Example Question #83 : Simplifying Exponents

Simplify: $\frac{6^{48}}{6^{12}}$ $\displaystyle \frac{6^{48}}{6^{12}}$

Possible Answers:

$6^{22}$ $\displaystyle 6^{22}$

$6{^{36}}$ $\displaystyle 6{^{36}}$

$6^{4}$ $\displaystyle 6^{4}$

$6^{30}$ $\displaystyle 6^{30}$

$6^{24}$ $\displaystyle 6^{24}$

Correct answer:

$6{^{36}}$ $\displaystyle 6{^{36}}$

Explanation:

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

$\frac{6^{48}}{6^{12}}=6^{48-12}=6^{36}$ $\displaystyle \frac{6^{48}}{6^{12}}=6^{48-12}=6^{36}$

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Example Question #84 : Simplifying Exponents

Simplify: $\frac{8^{60}}{8^{-12}}$ $\displaystyle \frac{8^{60}}{8^{-12}}$

Possible Answers:

$8^{-720}$ $\displaystyle 8^{-720}$

$8^{80}$ $\displaystyle 8^{80}$

$8^{72}$ $\displaystyle 8^{72}$

$8^{64}$ $\displaystyle 8^{64}$

$8^{48}$ $\displaystyle 8^{48}$

Correct answer:

$8^{72}$ $\displaystyle 8^{72}$

Explanation:

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

$\frac{8^{60}}{8^{-12}}=8^{60-(-12)}=8^{72}$ $\displaystyle \frac{8^{60}}{8^{-12}}=8^{60-(-12)}=8^{72}$

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Example Question #85 : Multiplying And Dividing Exponents

Simplify the following:

$\displaystyle (2a^2b^8c)(8bc^7)$

Possible Answers:

$\displaystyle 16a^2b^9c^8$

$\displaystyle 16a^2b^9c^7$

$\displaystyle 16b^9c^8$

$\displaystyle 16a^2b^8c^7$

$\displaystyle 16b^8c^7$

Correct answer:

$\displaystyle 16a^2b^9c^8$

Explanation:

Remembering the exponent rule of multiplication:

$x^m*x^n=x^{m+n}$ $\displaystyle x^m*x^n=x^{m+n}$

Therefore:

$\displaystyle (2a^2b^8c)(8bc^7)$

Becomes:

$2*8a^2b^{8+1}c^{1+7}$ $\displaystyle 2*8a^2b^{8+1}c^{1+7}$

Which gives the final answer:

$\displaystyle 16a^2b^9c^8$

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Example Question #86 : Simplifying Exponents

Simplify:

$\frac{12a^6b^2c^3}{4ab^7c^6}$ $\displaystyle \frac{12a^6b^2c^3}{4ab^7c^6}$

Possible Answers:

$\frac{3a^6b}{c^3}$ $\displaystyle \frac{3a^6b}{c^3}$

$\displaystyle 3a^5b^5c^3$

$\frac{a^5}{3b^5c^3}$ $\displaystyle \frac{a^5}{3b^5c^3}$

$\frac{4a^5}{b^5c^3}$ $\displaystyle \frac{4a^5}{b^5c^3}$

$\frac{3a^5}{b^5c^3}$ $\displaystyle \frac{3a^5}{b^5c^3}$

Correct answer:

$\frac{3a^5}{b^5c^3}$ $\displaystyle \frac{3a^5}{b^5c^3}$

Explanation:

Using the exponent rules:

$\frac{x^m}{x^n}=x^{m-n}$ $\displaystyle \frac{x^m}{x^n}=x^{m-n}$

and:

$x^{-m}=\frac{1}{x^m}$ $\displaystyle x^{-m}=\frac{1}{x^m}$

Gives:

$(12/4)a^{6-1}b^{2-7}c^{3-6}=3a^5b^{-5}c^{-3}=\frac{3a^5}{b^5c^3}$ $\displaystyle (12/4)a^{6-1}b^{2-7}c^{3-6}=3a^5b^{-5}c^{-3}=\frac{3a^5}{b^5c^3}$

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Example Question #85 : Simplifying Exponents

Simplify: $15^8*15^{12}$ $\displaystyle 15^8*15^{12}$

Possible Answers:

$15^{20}$ $\displaystyle 15^{20}$

$225^{96}$ $\displaystyle 225^{96}$

$15^{24}$ $\displaystyle 15^{24}$

$225^{20}$ $\displaystyle 225^{20}$

$15^{96}$ $\displaystyle 15^{96}$

Correct answer:

$15^{20}$ $\displaystyle 15^{20}$

Explanation:

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

$15^8*15^{12}=15^{8+12}=15^{20}$ $\displaystyle 15^8*15^{12}=15^{8+12}=15^{20}$

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Example Question #3551 : Algebra Ii

Simplify: $12^{-12}*12^{-9}$ $\displaystyle 12^{-12}*12^{-9}$

Possible Answers:

$12^{108}$ $\displaystyle 12^{108}$

$12^{-14}$ $\displaystyle 12^{-14}$

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

$12^{-21}$ $\displaystyle 12^{-21}$

12^7 $\displaystyle 12^7$

Correct answer:

$12^{-21}$ $\displaystyle 12^{-21}$

Explanation:

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

$12^{-12}*12^{-9}=12^{-12+(-9)}=12^{-21}$ $\displaystyle 12^{-12}*12^{-9}=12^{-12+(-9)}=12^{-21}$

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Example Question #3552 : Algebra Ii

Simplify: $3^{-10}*3^{19}$ $\displaystyle 3^{-10}*3^{19}$

Possible Answers:

$3^{-29}$ $\displaystyle 3^{-29}$

$3^{-19}$ $\displaystyle 3^{-19}$

3^7 $\displaystyle 3^7$

$3^{-90}$ $\displaystyle 3^{-90}$

3^9 $\displaystyle 3^9$

Correct answer:

3^9 $\displaystyle 3^9$

Explanation:

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

$3^{-10}*3^{19}=3^{-10+19}=3^9$ $\displaystyle 3^{-10}*3^{19}=3^{-10+19}=3^9$

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Example Question #3553 : Algebra Ii

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

Possible Answers:

$6^{48}$ $\displaystyle 6^{48}$

6^2 $\displaystyle 6^2$

$6^{44}$ $\displaystyle 6^{44}$

$6^{22}$ $\displaystyle 6^{22}$

$6^{11}$ $\displaystyle 6^{11}$

Correct answer:

$6^{44}$ $\displaystyle 6^{44}$

Explanation:

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

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

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Algebra II : Multiplying and Dividing Exponents

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #81 : Simplifying Exponents

Example Question #82 : Simplifying Exponents

Example Question #83 : Simplifying Exponents

Example Question #84 : Simplifying Exponents

Example Question #85 : Multiplying And Dividing Exponents

Example Question #86 : Simplifying Exponents

Example Question #85 : Simplifying Exponents

Example Question #3551 : Algebra Ii

Example Question #3552 : Algebra Ii

Example Question #3553 : Algebra Ii

All Algebra II Resources

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