Rational Exponents 3
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Question 1 of 5
1. Question
Simplify$$125^{-\frac{2}{3}}$$Write fractions as “a/b”- (1/25)
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.$$125^{-\color{#e65021}{\frac{2}{3}}}$$ `=` $$\frac{1}{125^\color{#e65021}{\frac{2}{3}}}$$ Next, simplify further using Fractional Powers.$$\frac{1}{125^{\frac{\color{#004ec4}{2}}{\color{#D800AD}{3}}}}$$ `=` $$\frac{1}{(\sqrt[\color{#D800AD}{3}]{125})^{\color{#004ec4}{2}}}$$ `=` `1/(5)^2` `root (3)(125)=5` `=` `1/(25)` `5^2=25` `1/(25)` -
Question 2 of 5
2. Question
Simplify`[8^(2/3)]^(1/2)`- (2)
Hint
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Power of a Power
$${(a^\color{#007DDC}{m})}^{\color{#9a00c7}{n}}=a^{\color{#007DDC}{m} \times \color{#9a00c7}{n}}$$Fractional Powers
$$a^{\frac{\color{#004ec4}{T}}{\color{#D800AD}{B}}}=(\sqrt[\color{#D800AD}{B}]{a})^{\color{#004ec4}{T}}$$First, use Power of a Power to simplify the expression.$${[8^{\color{#007DDC}{\frac{2}{3}}})}^\color{#9a00c7}{\frac{1}{2}}$$ `=` $$8^{{\color{#007DDC}{\frac{2}{3}}} \times {\color{#9a00c7}{\frac{1}{2}}}}$$ `=` $$8^{\frac{2}{6}}$$ `=` $$8^{\frac{1}{3}}$$ Simplify Next, simplify further using Fractional Powers.$$8^{\frac{\color{#004ec4}{1}}{\color{#D800AD}{3}}}$$ `=` $$(\sqrt[\color{#D800AD}{3}]{8})^{\color{#004ec4}{1}}$$ `=` `(2)^1` `root (3)(8)=2` `=` `2` `2^1=2` `2` -
Question 3 of 5
3. Question
Simplify`(32x)^(2/5)`Hint
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Power of a Power
$${(a^\color{#007DDC}{m})}^{\color{#9a00c7}{n}}=a^{\color{#007DDC}{m} \times \color{#9a00c7}{n}}$$Fractional Powers
$$a^{\frac{\color{#004ec4}{T}}{\color{#D800AD}{B}}}=(\sqrt[\color{#D800AD}{B}]{a})^{\color{#004ec4}{T}}$$First, use Power of a Power to simplify the expression.$$(32x)^\color{#9a00c7}{\frac{2}{5}}$$ `=` $$32^{\color{#9a00c7}{\frac{2}{5}}} \times x^{\color{#9a00c7}{\frac{2}{5}}}$$ Next, simplify further using Fractional Powers.$$32^{\frac{\color{#004ec4}{2}}{\color{#D800AD}{5}}} \times x^{\frac{2}{5}}$$ `=` $$(\sqrt[\color{#D800AD}{5}]{32})^{\color{#004ec4}{2}} \times x^{\frac{2}{5}}$$ `=` `(2)^2 xx x^(2/5)` `root (5)(32)=2` `=` `4x^(2/5)` `2^2=4` `4x^(2/5)` -
Question 4 of 5
4. Question
Simplify`(64a^(12))^(4/3)`Hint
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Power of a Power
$${(a^\color{#007DDC}{m})}^{\color{#9a00c7}{n}}=a^{\color{#007DDC}{m} \times \color{#9a00c7}{n}}$$Fractional Powers
$$a^{\frac{\color{#004ec4}{T}}{\color{#D800AD}{B}}}=(\sqrt[\color{#D800AD}{B}]{a})^{\color{#004ec4}{T}}$$First, use Power of a Power to simplify the expression.$$(64a^{\color{#007DDC}{12}})^\color{#9a00c7}{\frac{4}{3}}$$ `=` $$64^{\color{#9a00c7}{\frac{4}{3}}} \times a^{\color{#007DDC}{12} \times \color{#9a00c7}{\frac{4}{3}}}$$ `=` `64^(4/3) xx a^((48)/3)` `=` `64^(4/3) xx a^(16)` Simplify Next, simplify further using Fractional Powers.$$64^{\frac{\color{#004ec4}{4}}{\color{#D800AD}{3}}} \times a^{16}$$ `=` $$(\sqrt[\color{#D800AD}{3}]{64})^{\color{#004ec4}{4}} \times a^{16}$$ `=` `(4)^4 xx a^(16)` `root (3)(64)=4` `=` `256a^(16)` `4^4=256` `256a^(16)` -
Question 5 of 5
5. Question
Simplify`(25w^(10))^(3/2)`Hint
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Power of a Power
$${(a^\color{#007DDC}{m})}^{\color{#9a00c7}{n}}=a^{\color{#007DDC}{m} \times \color{#9a00c7}{n}}$$Fractional Powers
$$a^{\frac{\color{#004ec4}{T}}{\color{#D800AD}{B}}}=(\sqrt[\color{#D800AD}{B}]{a})^{\color{#004ec4}{T}}$$First, use Power of a Power to simplify the expression.$$(25w^{\color{#007DDC}{10}})^\color{#9a00c7}{\frac{3}{2}}$$ `=` $$25^{\color{#9a00c7}{\frac{3}{2}}} \times w^{\color{#007DDC}{10} \times \color{#9a00c7}{\frac{3}{2}}}$$ `=` `25^(3/2) xx w^((30)/2)` `=` `25^(3/2) xx w^(15)` Simplify Next, simplify further using Fractional Powers.$$25^{\frac{\color{#004ec4}{3}}{\color{#D800AD}{2}}} \times w^{15}$$ `=` $$(\sqrt[\color{#D800AD}{2}]{25})^{\color{#004ec4}{3}} \times w^{15}$$ `=` `(5)^3 xx w^(15)` `root (2)(25)=5` `=` `125w^(15)` `5^3=125` `125w^(15)`
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