Answer:
4. [tex]x^{(\frac{7}{4})} = \sqrt[7]{x^4}[/tex]
Step-by-step explanation:
Here, consider the each expression and simplify it:
1.[tex]x^{\frac{1}{8} }\times x^{\frac{1}{8}[/tex]
Now, if the BASE IS SAME when multiplied, THE POWERS ARE ADDED.
[tex]x^{\frac{1}{8} }\times x^{\frac{1}{8}} = x^{(\frac{1}{8} + \frac{1}{8})}\\= x^{(\frac{1}{4})} =\sqrt[4]{x} \\\implies x^{\frac{1}{8} }\times x^{\frac{1}{8}} = \sqrt[4]{x}[/tex]
Hence, given statement if TRUE.
2. [tex]\frac{x^{\frac{2}{5} }}{x^{\frac{1}{5} }}[/tex]
Now, if the BASE IS SAME when divided, THE POWERS ARE SUBTRACTED.
[tex]\frac{x^{\frac{2}{5} }}{x^{\frac{1}{5} }} = x^{(\frac{2}{5} ) -(\frac{1}{5} )} = x^ {(\frac{1}{5})} = \sqrt[5]{x} \\\implies \frac{x^{\frac{2}{5} }}{x^{\frac{1}{5} }} = \sqrt[5]{x}[/tex]
Hence, given statement if TRUE.
3. [tex]x^{(\frac{7}{9})[/tex]
Now,a s we know : [tex]x^{(\frac{1}{a}) } = \sqrt[a]{x}[/tex]
So, solving given expression: [tex]x^{(\frac{7}{9})} = \sqrt[9]{x^7}[/tex]
Hence, given statement if TRUE.
4. [tex]x^{(\frac{7}{4})[/tex]
Now,a s we know : [tex]x^{(\frac{1}{a}) } = \sqrt[a]{x}[/tex]
So, solving given expression: [tex]x^{(\frac{7}{4})} = \sqrt[4]{x^7} \neq \sqrt[7]{x^4}[/tex]
Hence, given statement if FALSE.
