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Question 1 of 6
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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`
Question 2 of 6
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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`
Question 3 of 6
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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`
Question 4 of 6
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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`
Question 5 of 6
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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`
Question 6 of 6
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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`