Divide Indices 1
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Question 1 of 4
1. Question
Simplify`x^8 -: x^2`Hint
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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 Quotient of Powers, bring similar bases together.$$\color{#00880A}{x}^8 \div \color{#00880A}{x}^2$$ `=` $$\color{#00880A}{x}^{8-2}$$ `=` `x^6` `x^6` -
Question 2 of 4
2. Question
Simplify`(6^10)/(6^3)`Hint
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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 Quotient of Powers, bring similar bases together.$$\frac{{\color{#00880A}{6}^{10}}}{{\color{#00880A}{6}^3}}$$ `=` $$\color{#00880A}{6}^{10-3}$$ `=` `6^7` `6^7` -
Question 3 of 4
3. Question
Simplify`((-4)^5)/((-4)^2)`Hint
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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 Quotient of Powers, bring similar bases together.$$\frac{{(\color{#00880A}{-4})^5}}{{(\color{#00880A}{-4})^2}}$$ `=` $$(\color{#00880A}{-4})^{5-2}$$ `=` `(-4)^3` `(-4)^3` -
Question 4 of 4
4. Question
Simplify`(3^4 xx 3^8)/(3^7)`Hint
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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.`(3^4 xx 3^8)/(3^7)` `=` $$\frac{\color{#00880A}{3}^4 \times \color{#00880A}{3}^8}{3^7}$$ `=` $$\frac{\color{#00880A}{3}^{4+8}}{3^7}$$ `=` $$\frac{\color{#00880A}{3}^{12}}{3^7}$$ Simplify further using the Quotient of Powers.$$\frac{\color{#00880A}{3}^{12}}{\color{#00880A}{3}^7}$$ `=` $$\color{#00880A}{3}^{12-7}$$ `=` `3^5` `3^5`
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