Rational Exponents 2
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Question 1 of 6
1. Question
Simplify`16^(3/4)`- (8)
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Fractional Powers
$$a^{\frac{\color{#004ec4}{T}}{\color{#D800AD}{B}}}=(\sqrt[\color{#D800AD}{B}]{a})^{\color{#004ec4}{T}}$$Use Fractional Powers to simplify the expression.$$16^{\frac{\color{#004ec4}{3}}{\color{#D800AD}{4}}}$$ `=` $$(\sqrt[\color{#D800AD}{4}]{16})^{\color{#004ec4}{3}}$$ `=` `(2)^3` `root (4)(16)=2` `=` `8` `8` -
Question 2 of 6
2. Question
Simplify`125^(1/3)`- (5)
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Fractional Powers
$$a^{\frac{\color{#004ec4}{T}}{\color{#D800AD}{B}}}=(\sqrt[\color{#D800AD}{B}]{a})^{\color{#004ec4}{T}}$$Use Fractional Powers to simplify the expression.$$125^{\frac{\color{#004ec4}{1}}{\color{#D800AD}{3}}}$$ `=` $$(\sqrt[\color{#D800AD}{3}]{125})^{\color{#004ec4}{1}}$$ `=` `(5)^1` `root (3)(125)=5` `=` `5` `5` -
Question 3 of 6
3. Question
Simplify`xsqrtx`Hint
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Fractional Powers
$$\sqrt[\color{#D800AD}{B}]{a^{\color{#004ec4}{T}}}=a^{\frac{\color{#004ec4}{T}}{\color{#D800AD}{B}}}$$Product of Powers
$${\color{#00880A}{a}^m}\times{\color{#00880A}{a}^n}=\color{#00880A}{a}^{m+n}$$Fractional Powers
$$(\sqrt[\color{#D800AD}{B}]{a})^{\color{#004ec4}{T}}=a^{\frac{\color{#004ec4}{T}}{\color{#D800AD}{B}}}$$Use Fractional Powers to simplify the expression.$$x^1\sqrt[\color{#D800AD}{2}]{27^{\color{#004ec4}{1}}}$$ `=` $$x^1 \times x^{\frac{\color{#004ec4}{1}}{\color{#D800AD}{2}}}$$ Next, use the Product of Powers to simplify the expression further.$$\color{#00880A}{x}^1 \times \color{#00880A}{x}^{\frac{1}{2}}$$ `=` $$\color{#00880A}{x}^{1+\frac{1}{2}}$$ `=` $$\color{#00880A}{x}^{1\frac{1}{2}}$$ `=` `x^(3/2)` Convert the power into a fraction `x^(3/2)` -
Question 4 of 6
4. Question
Simplify$$16^{-\frac{1}{2}}$$Write fractions as “a/b”- (1/4)
Hint
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Negative Power
$$a^{-\color{#e65021}{n}}=\frac{1}{a^\color{#e65021}{n}}$$Fractional Powers
$$a^{\frac{\color{#004ec4}{T}}{\color{#D800AD}{B}}}=(\sqrt[\color{#D800AD}{B}]{a})^{\color{#004ec4}{T}}$$First, use Negative Powers to simplify the expression.$$16^{-\color{#e65021}{\frac{1}{2}}}$$ `=` $$\frac{1}{16^\color{#e65021}{\frac{1}{2}}}$$ Next, simplify further using Fractional Powers.$$\frac{1}{16^{\frac{\color{#004ec4}{1}}{\color{#D800AD}{2}}}}$$ `=` $$\frac{1}{(\sqrt[\color{#D800AD}{2}]{16})^{\color{#004ec4}{1}}}$$ `=` `1/(4)^1` `root (2)(16)=4` `=` `1/4` `4^1=4` `1/4` -
Question 5 of 6
5. Question
Simplify$$4^{-\frac{3}{2}}$$Write fractions as “a/b”- (1/8)
Hint
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Negative Power
$$a^{-\color{#e65021}{n}}=\frac{1}{a^\color{#e65021}{n}}$$Fractional Powers
$$a^{\frac{\color{#004ec4}{T}}{\color{#D800AD}{B}}}=(\sqrt[\color{#D800AD}{B}]{a})^{\color{#004ec4}{T}}$$First, use Negative Powers to simplify the expression.$$4^{-\color{#e65021}{\frac{3}{2}}}$$ `=` $$\frac{1}{4^\color{#e65021}{\frac{3}{2}}}$$ Next, simplify further using Fractional Powers.$$\frac{1}{4^{\frac{\color{#004ec4}{3}}{\color{#D800AD}{2}}}}$$ `=` $$\frac{1}{(\sqrt[\color{#D800AD}{2}]{4})^{\color{#004ec4}{3}}}$$ `=` `1/(2)^3` `root (2)(4)=2` `=` `1/8` `2^3=8` `1/8` -
Question 6 of 6
6. Question
Simplify$$8^{-\frac{4}{3}}$$Write fractions as “a/b”- (1/16)
Hint
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Negative Power
$$a^{-\color{#e65021}{n}}=\frac{1}{a^\color{#e65021}{n}}$$Fractional Powers
$$a^{\frac{\color{#004ec4}{T}}{\color{#D800AD}{B}}}=(\sqrt[\color{#D800AD}{B}]{a})^{\color{#004ec4}{T}}$$First, use Negative Powers to simplify the expression.$$8^{-\color{#e65021}{\frac{4}{3}}}$$ `=` $$\frac{1}{8^\color{#e65021}{\frac{4}{3}}}$$ Next, simplify further using Fractional Powers.$$\frac{1}{8^{\frac{\color{#004ec4}{4}}{\color{#D800AD}{3}}}}$$ `=` $$\frac{1}{(\sqrt[\color{#D800AD}{3}]{8})^{\color{#004ec4}{4}}}$$ `=` `1/(2)^4` `root (3)(8)=2` `=` `1/(16)` `2^4=16` `1/(16)`
Quizzes
- Exponent Notation 1
- Exponent Notation 2
- Exponent Notation 3
- Multiply Exponents (Product Rule) 1
- Multiply Exponents (Product Rule) 2
- Multiply Exponents (Product Rule) 3
- Multiply Exponents (Product Rule) 4
- Divide Exponents (Quotient Rule) 1
- Divide Exponents (Quotient Rule) 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 Exponents 1
- Negative Exponents 2
- Negative Exponents 3
- Rational Exponents 1
- Rational Exponents 2
- Rational Exponents 3
- Mixed Operations with Exponents 1
- Mixed Operations with Exponents 2