Rational Exponents 1
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Question 1 of 6
1. Question
Simplify`a^(T/B)`Hint
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Simplify`64^(2/3)`Incorrect
Identify the known lengths
`\text(Base)=a``\text(Numerator/Top)=T``\text(Denominator/Bottom)=B`To simplify a fractional power, use the denominator/bottom value `B` as a root and use the numerator/top value `T` as the power.$$a^{\frac{\color{#004ec4}{T}}{\color{#D800AD}{B}}}$$ `=` $$\sqrt[\color{#D800AD}{B}]{a^{\color{#004ec4}{T}}}$$ To remember this easily, take note that `B` comes before `T` alphabetically. This means that `B` will be at the left side(the root) and `T` will be at the right side (the power).`root(B)(a^T)` can also be written as `(root(B)(a))^T``root(B)(a^T)` -
Question 2 of 6
2. Question
Simplify`64^(2/3)`- (16)
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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.$$64^{\frac{\color{#004ec4}{2}}{\color{#D800AD}{3}}}$$ `=` $$(\sqrt[\color{#D800AD}{3}]{64})^{\color{#004ec4}{2}}$$ `=` `(4)^2` `root (3)(64)=4` `=` `16` `16` -
Question 3 of 6
3. Question
Simplify`27^(1/3)`- (3)
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Incorrect
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.$$27^{\frac{\color{#004ec4}{1}}{\color{#D800AD}{3}}}$$ `=` $$(\sqrt[\color{#D800AD}{3}]{27})^{\color{#004ec4}{1}}$$ `=` `(3)^1` `root (3)(27)=3` `=` `3` `3` -
Question 4 of 6
4. Question
Simplify`9^(1/2)`- (3)
Hint
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Incorrect
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.$$9^{\frac{\color{#004ec4}{1}}{\color{#D800AD}{2}}}$$ `=` $$(\sqrt[\color{#D800AD}{2}]{9})^{\color{#004ec4}{1}}$$ `=` `(3)^1` `root (2)(9)=3` `=` `3` `3` -
Question 5 of 6
5. Question
Simplify`25^(3/2)`- (125)
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Incorrect
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.$$25^{\frac{\color{#004ec4}{3}}{\color{#D800AD}{2}}}$$ `=` $$(\sqrt[\color{#D800AD}{2}]{25})^{\color{#004ec4}{3}}$$ `=` `(5)^3` `root (2)(25)=5` `=` `125` `125` -
Question 6 of 6
6. Question
Simplify`9^(3/2)`- (27)
Hint
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Excellent!
Incorrect
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.$$9^{\frac{\color{#004ec4}{3}}{\color{#D800AD}{2}}}$$ `=` $$(\sqrt[\color{#D800AD}{2}]{9})^{\color{#004ec4}{3}}$$ `=` `(3)^3` `root (2)(9)=3` `=` `27` `27`
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