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Which of the following choices are equivalent to the expression below? Check all that applyx^(3/8)

Which Of The Following Choices Are Equivalent To The Expression Below Check All That Applyx38 class=

Sagot :

Answer: [tex]\begin{gathered} \text{\lparen}\sqrt[8]{x^3}\text{ \rparen \lparen option B\rparen} \\ \\ \text{\lparen}\sqrt[8]{x^\text{\rparen}^3}\text{ \lparen option D\rparen} \\ \\ (x^3)\placeholder{⬚}^{\frac{1}{8}}\text{ \lparen option F\rparen} \end{gathered}[/tex]

Explanation:

Given:

[tex]x^{\frac{3}{8}}[/tex]

To find:

the equivalence of the given expression

[tex]\begin{gathered} We\text{ will apply exponent rule:} \\ x^{\frac{1}{b}}\text{ = }\sqrt[b]{x} \\ x^{\frac{a}{b}}\text{ = \lparen}\sqrt[b]{x})\placeholder{⬚}^a \\ \\ Applying\text{ same rule to the given expression:} \\ x^{\frac{3}{8}}\text{ = \lparen}\sqrt[8]{x})\placeholder{⬚}^3 \end{gathered}[/tex][tex]\begin{gathered} (\sqrt[8]{x})\placeholder{⬚}^3\text{ can also be written as \lparen}\sqrt[8]{x^3}) \\ x^{\frac{3}{8}}=\text{ \lparen}\sqrt[8]{x^3}\text{ \rparen} \end{gathered}[/tex][tex]\begin{gathered} from\text{ \lparen}\sqrt[8]{x})\placeholder{⬚}^3,\text{ }\sqrt[8]{x}\text{ = x}^{\frac{1}{8}} \\ \\ (\sqrt[8]{x})\placeholder{⬚}^3\text{ = \lparen x}^{\frac{1}{8}})\placeholder{⬚}^3 \\ =(\text{x}^3)\placeholder{⬚}^{\frac{1}{8}} \end{gathered}[/tex]

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