Question

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

Answer 1

Answer:
`\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{⬚}^{(1)/(8)}\text{ \lparen option F\rparen} \end{gathered}`

Step-by-step explanation:

Given:

`x^{(3)/(8)}`

To find:

the equivalence of the given expression

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