Divide Indices 2
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Question 1 of 4
1. Question
Simplify`(3^(-5))/(3^(-2))`Write fractions as “a/b”- (1/27)
Hint
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Nice Job!
Incorrect
Quotient of Powers
$${\color{#00880A}{a}^m}\div{\color{#00880A}{a}^n}=\frac{{\color{#00880A}{a}^m}}{{\color{#00880A}{a}^n}}=\color{#00880A}{a}^{m-n}$$Negative Powers
$$a^{-\color{#e65021}{n}}=\frac{1}{a^\color{#e65021}{n}}$$Using the Quotient of Powers, bring similar bases together.$$\frac{\color{#00880A}{3}^{-5}}{\color{#00880A}{3}^{-2}}$$ `=` $$\color{#00880A}{3}^{(-5)-(-2)}$$ `=` $$\color{#00880A}{3}^{(-5)+2}$$ `=` `3^(-3)` Use Negative Powers to further simplify the expression.$$3^{\color{#e65021}{-3}}$$ `=` $$\frac{1}{3^{\color{#e65021}{3}}}$$ `=` `1/(27)` `3 xx 3 xx 3 = 27` `1/(27)` -
Question 2 of 4
2. Question
Simplify`7a^6 b^2 -: 4ab^2`Hint
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Quotient of Powers
$${\color{#00880A}{a}^m}\div{\color{#00880A}{a}^n}=\frac{{\color{#00880A}{a}^m}}{{\color{#00880A}{a}^n}}=\color{#00880A}{a}^{m-n}$$Power of Zero
Anything to the power of zero becomes `1`.First, bring the like terms together`7a^6 b^2 -: 4ab^2` `=` `(7/4)xx((a^6)/a)xx((b^2)/(b^2))` Using the Quotient of Powers, bring similar bases together.$$\frac{7}{4} \times \frac{\color{#00880A}{a}^6}{\color{#00880A}{a}^1} \times \frac{\color{#9a00c7}{b}^2}{\color{#9a00c7}{b}^2}$$ `=` $$\frac{7}{4} \times \color{#00880A}{a}^{6-1} \times \color{#9a00c7}{b}^{2-2}$$ `=` $$\frac{7}{4} \times \color{#00880A}{a}^5 \times \color{#9a00c7}{b}^0$$ `=` `7/4 xx a^5 xx 1` `b^0=1` `=` `(7a^5)/4` `(7a^5)/4` -
Question 3 of 4
3. Question
Simplify`(14m^2y)/(2my^2)`Write fractions as “a/b”- (7m/y)
Hint
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Fantastic!
Incorrect
Quotient of Powers
$${\color{#00880A}{a}^m}\div{\color{#00880A}{a}^n}=\frac{{\color{#00880A}{a}^m}}{{\color{#00880A}{a}^n}}=\color{#00880A}{a}^{m-n}$$Negative Powers
$$a^{-\color{#e65021}{n}}=\frac{1}{a^\color{#e65021}{n}}$$First, bring the like terms together`(14m^2y)/(2my^2)` `=` `(14/2)xx((m^2)/m)xx((y)/(y^2))` Using the Quotient of Powers, bring similar bases together.$$\frac{14}{2} \times \frac{\color{#00880A}{m}^2}{\color{#00880A}{m}^1} \times \frac{\color{#9a00c7}{y}^1}{\color{#9a00c7}{y}^2}$$ `=` $$7 \times \color{#00880A}{m}^{2-1} \times \color{#9a00c7}{y}^{1-2}$$ `=` `7my^(-1)` Use Negative Powers to further simplify the expression.$$7my^{\color{#e65021}{-1}}$$ `=` $$\frac{7m}{y^{\color{#e65021}{1}}}$$ `=` `(7m)/y` A power of `1` does not need to be written `(7m)/y` -
Question 4 of 4
4. Question
If `A=21x^5 y^3`, find the width of this rectangle:
Hint
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Well done!
Incorrect
Quotient of Powers
$${\color{#00880A}{a}^m}\div{\color{#00880A}{a}^n}=\frac{{\color{#00880A}{a}^m}}{{\color{#00880A}{a}^n}}=\color{#00880A}{a}^{m-n}$$Area of a Rectangle
`A=L xx W`Since we are looking for the Width, we can take the Area formula and make Width (`W`) the subject.`A` `=` `LxxW` `A``-:L` `=` `LxxW``-:L` Divide both sides by `L` `A/L` `=` `W` `W` `=` `A/L` Substitute the known values.`A=21x^5 y^3``L=7x^3 y^2``W` `=` `A/L` `=` `(21x^5 y^3)/(7x^3 y^2)` `=` `21/7 xx (x^5)/(x^3) xx (y^3)/(y^2)` Join similar terms `=` $$3 \times \frac{\color{#00880A}{x}^5}{\color{#00880A}{x}^3} \times \frac{\color{#9a00c7}{y}^3}{\color{#9a00c7}{y}^2}$$ Simplify using Quotient of Powers `=` $$3\color{#00880A}{x}^{(5-3)}\color{#9a00c7}{y}^{(3-2)}$$ `=` `3x^2 y` `3x^2 y`
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