Index Notation 3
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Question 1 of 5
1. Question
Simplify`6 xx a^2 xx 4a^3 xx a`Hint
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Product of Powers
$${\color{#00880A}{a}^m}\times{\color{#00880A}{a}^n}=\color{#00880A}{a}^{m+n}$$First, separate the numbers and the variables and bring like terms together.`6 xx a^2 xx 4a^3 xx a` `=` `6 xx a^2 xx 4 xx a^3 xx a` `=` `6 xx 4 xx a^2 xx a^3 xx a` Next, using the Product of Powers, bring similar bases together.Remember that any base without a power means to the power of `1`.`6 xx 4 xx a^2 xx a^3 xx a` `=` `6^1``xx``4^1``xx``a^2``xx``a^3``xx``a^1` `=` $$\color{#00880A}{24} \times \color{#9a00c7}{a}^{2+3+1}$$ `=` $$\color{#00880A}{24} \times \color{#9a00c7}{a}^6$$ `=` `24a^6` `24a^6` -
Question 2 of 5
2. Question
Simplify`(a xx a xx a xx a)/(a xx a)`Hint
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Great Work!
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Product of Powers
$${\color{#00880A}{a}^m}\times{\color{#00880A}{a}^n}=\color{#00880A}{a}^{m+n}$$Quotient of Powers
$${\color{#00880A}{a}^m}\div{\color{#00880A}{a}^n}=\frac{{\color{#00880A}{a}^m}}{{\color{#00880A}{a}^n}}=\color{#00880A}{a}^{m-n}$$Using the Product of Powers, bring similar bases together.Remember that any base without a power means to the power of `1`.`(a xx a xx a xx a)/(a xx a)` `=` $$\frac{\color{#00880A}{a}^1 \times \color{#00880A}{a}^1 \times \color{#00880A}{a}^1 \times \color{#00880A}{a}^1}{\color{#00880A}{a}^1 \times \color{#00880A}{a}^1}$$ `=` $$\frac{\color{#00880A}{a}^{1+1+1+1}}{\color{#00880A}{a}^{1+1}}$$ `=` $$\frac{\color{#00880A}{a}^4}{\color{#00880A}{a}^2}$$ Simplify further using the Quotient of Powers.$$\frac{\color{#00880A}{a}^4}{\color{#00880A}{a}^2}$$ `=` $$\color{#00880A}{a}^{4-2}$$ `=` `a^2` `a^2` -
Question 3 of 5
3. Question
Simplify`(4c xx c xx c)/(c xx c)`- (4c)
Hint
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Correct!
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Product of Powers
$${\color{#00880A}{a}^m}\times{\color{#00880A}{a}^n}=\color{#00880A}{a}^{m+n}$$Quotient of Powers
$${\color{#00880A}{a}^m}\div{\color{#00880A}{a}^n}=\frac{{\color{#00880A}{a}^m}}{{\color{#00880A}{a}^n}}=\color{#00880A}{a}^{m-n}$$Using the Product of Powers, bring similar bases together.Remember that any base without a power means to the power of `1`.`(4c xx c xx c)/(c xx c)` `=` $$\frac{4 \times \color{#00880A}{c}^1 \times \color{#00880A}{c}^1 \times \color{#00880A}{c}^1}{\color{#00880A}{c}^1 \times \color{#00880A}{c}^1}$$ `=` $$\frac{4 \times \color{#00880A}{c}^{1+1+1}}{\color{#00880A}{c}^{1+1}}$$ `=` $$\frac{4 \times \color{#00880A}{c}^3}{\color{#00880A}{c}^2}$$ Simplify further using the Quotient of Powers.$$\frac{4 \times \color{#00880A}{c}^3}{\color{#00880A}{c}^2}$$ `=` $$4\color{#00880A}{c}^{3-2}$$ `=` `4c` A power of `1` does not need to be written `4c` -
Question 4 of 5
4. Question
Simplify`(3 xx y xx y xx y xx z xx z xxz)/(y xx y)`Hint
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Nice Job!
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Product of Powers
$${\color{#00880A}{a}^m}\times{\color{#00880A}{a}^n}=\color{#00880A}{a}^{m+n}$$Quotient of Powers
$${\color{#00880A}{a}^m}\div{\color{#00880A}{a}^n}=\frac{{\color{#00880A}{a}^m}}{{\color{#00880A}{a}^n}}=\color{#00880A}{a}^{m-n}$$Using the Product of Powers, bring similar bases together.Remember that any base without a power means to the power of `1`.`(3 xx y xx y xx y xx z xx z xxz)/(y xx y)` `=` $$\frac{3 \times \color{#00880A}{y}^1 \times \color{#00880A}{y}^1 \times \color{#00880A}{y}^1 \times \color{#9a00c7}{z}^1 \times \color{#9a00c7}{z}^1 \times \color{#9a00c7}{z}^1}{\color{#00880A}{y}^1 \times \color{#00880A}{y}^1}$$ `=` $$\frac{3 \times \color{#00880A}{y}^{1+1+1} \times \color{#9a00c7}{z}^{1+1+1}}{\color{#00880A}{y}^{1+1}}$$ `=` $$\frac{3 \times \color{#00880A}{y}^3 \times \color{#9a00c7}{z}^3}{\color{#00880A}{y}^2}$$ Simplify further using the Quotient of Powers.$$\frac{3 \times \color{#00880A}{y}^3 \times \color{#9a00c7}{z}^3}{\color{#00880A}{y}^2}$$ `=` $$3\color{#00880A}{y}^{3-2} \times \color{#9a00c7}{z}^3$$ `=` `3yz^3` A power of `1` does not need to be written `3yz^3` -
Question 5 of 5
5. Question
Simplify`(5a xx 2a xx a xx a xx a)/(a^2)`Hint
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Excellent!
Incorrect
Product of Powers
$${\color{#00880A}{a}^m}\times{\color{#00880A}{a}^n}=\color{#00880A}{a}^{m+n}$$Quotient of Powers
$${\color{#00880A}{a}^m}\div{\color{#00880A}{a}^n}=\frac{{\color{#00880A}{a}^m}}{{\color{#00880A}{a}^n}}=\color{#00880A}{a}^{m-n}$$Using the Product of Powers, bring similar bases together.Remember that any base without a power means to the power of `1`.`(5a xx 2a xx a xx a xx a)/(a^2)` `=` $$\frac{5 \times 2 \times \color{#00880A}{a}^1 \times \color{#00880A}{a}^1 \times \color{#00880A}{a}^1 \times \color{#00880A}{a}^1 \times \color{#00880A}{a}^1}{a^2}$$ `=` $$\frac{10 \times \color{#00880A}{a}^{1+1+1+1+1}}{a^2}$$ `=` $$\frac{10 \times \color{#00880A}{a}^5}{a^2}$$ Simplify further using the Quotient of Powers.$$\frac{10 \times \color{#00880A}{a}^5}{a^2}$$ `=` $$10\color{#00880A}{a}^{5-2}$$ `=` `10a^3` `10a^3`
Quizzes
- Index Notation 1
- Index Notation 2
- Index Notation 3
- Multiply Indices 1
- Multiply Indices 2
- Multiply Indices 3
- Multiply Indices 4
- Divide Indices 1
- Divide Indices 2
- Powers of a Power 1
- Powers of a Power 2
- Powers of a Power 3
- Powers of a Power 4
- Zero Powers 1
- Zero Powers 2
- Negative Indices 1
- Negative Indices 2
- Negative Indices 3
- Fractional Indices 1
- Fractional Indices 2
- Fractional Indices 3
- Mixed Operations with Indices 1
- Mixed Operations with Indices 2