Multiply Indices 3
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Question 1 of 4
1. Question
Simplify`3y^2 xx 4y^5`Hint
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Product of Powers
$${\color{#00880A}{a}^m}\times{\color{#00880A}{a}^n}=\color{#00880A}{a}^{m+n}$$First, bring the same bases together.`3y^2 xx 4y^5` `=` `3 xx 4 xx y^2 xx y^5` Using the Product of Powers, bring similar bases together.$$\color{#00880A}{3}^1 \times \color{#00880A}{4}^1 \times \color{#9a00c7}{y}^2 \times \color{#9a00c7}{y}^5$$ `=` $$\color{#00880A}{12} \times \color{#9a00c7}{y}^{2+5}$$ `=` `12y^7` `12y^7` -
Question 2 of 4
2. Question
Simplify`6m^7 xx 5m^3`Hint
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Product of Powers
$${\color{#00880A}{a}^m}\times{\color{#00880A}{a}^n}=\color{#00880A}{a}^{m+n}$$First, bring the same bases together.`6m^7 xx 5m^3` `=` `6 xx 5 xx m^7 xx m^3` Using the Product of Powers, bring similar bases together.$$\color{#00880A}{6}^1 \times \color{#00880A}{5}^1 \times \color{#9a00c7}{m}^7 \times \color{#9a00c7}{m}^3$$ `=` $$\color{#00880A}{30} \times \color{#9a00c7}{m}^{7+3}$$ `=` `30m^(10)` `30m^(10)` -
Question 3 of 4
3. Question
Simplify`6m^2 n xx 3m^4 n^2`Hint
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Product of Powers
$${\color{#00880A}{a}^m}\times{\color{#00880A}{a}^n}=\color{#00880A}{a}^{m+n}$$First, bring the same bases together.`6m^2 n xx 3m^4 n^2` `=` `6 xx 3 xx m^2 xx m^4 xx n xx n^2` Using the Product of Powers, bring similar bases together.$$\color{#00880A}{6}^1 \times \color{#00880A}{3}^1 \times \color{#9a00c7}{m}^2 \times \color{#9a00c7}{m}^4 \times \color{#e65021}{n}^1 \times \color{#e65021}{n}^2$$ `=` $$\color{#00880A}{18} \times \color{#9a00c7}{m}^{2+4} \times \color{#e65021}{n}^{1+2}$$ `=` `18m^6 n^3` `18m^6 n^3` -
Question 4 of 4
4. Question
Simplify`7ab^3 xx 2a^3 b`Hint
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Product of Powers
$${\color{#00880A}{a}^m}\times{\color{#00880A}{a}^n}=\color{#00880A}{a}^{m+n}$$First, bring the same bases together.`7ab^3 n xx 2a^3 b` `=` `7 xx 2 xx a xx a^3 xx b^3 xx b` Using the Product of Powers, bring similar bases together.$$\color{#00880A}{7}^1 \times \color{#00880A}{2}^1 \times \color{#9a00c7}{a}^1 \times \color{#9a00c7}{a}^3 \times \color{#e65021}{b}^3 \times \color{#e65021}{b}^1$$ `=` $$\color{#00880A}{14} \times \color{#9a00c7}{a}^{1+3} \times \color{#e65021}{b}^{3+1}$$ `=` `14a^4 b^4` `14a^4 b^4`
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