Question

Question in the below, i know it’s NOT A

Answer 1

Answer:

4. $x^{(\frac{7}{4})} = \sqrt[7]{x^4}$

Step-by-step explanation:

Here, consider the each expression and simplify it:

1.$x^{\frac{1}{8} }\times x^{\frac{1}{8}$

Now, if the BASE IS SAME when multiplied, THE POWERS ARE ADDED.

$x^{\frac{1}{8} }\times x^{\frac{1}{8}} = x^{(\frac{1}{8} + \frac{1}{8})}\\= x^{(\frac{1}{4})} =\sqrt[4]{x} \\\implies x^{\frac{1}{8} }\times x^{\frac{1}{8}} = \sqrt[4]{x}$

Hence, given statement if TRUE.

2. $\frac{x^{\frac{2}{5} }}{x^{\frac{1}{5} }}$

Now, if the BASE IS SAME when divided, THE POWERS ARE SUBTRACTED.

$\frac{x^{\frac{2}{5} }}{x^{\frac{1}{5} }} = x^{(\frac{2}{5} ) -(\frac{1}{5} )} = x^ {(\frac{1}{5})} = \sqrt[5]{x} \\\implies \frac{x^{\frac{2}{5} }}{x^{\frac{1}{5} }} = \sqrt[5]{x}$

Hence, given statement if TRUE.

3. $x^{(\frac{7}{9})$

Now,a s we know : $x^{(\frac{1}{a}) } = \sqrt[a]{x}$

So, solving given expression:  $x^{(\frac{7}{9})} = \sqrt[9]{x^7}$

Hence, given statement if TRUE.

4. $x^{(\frac{7}{4})$

Now,a s we know : $x^{(\frac{1}{a}) } = \sqrt[a]{x}$

So, solving given expression:  $x^{(\frac{7}{4})} = \sqrt[4]{x^7} \neq \sqrt[7]{x^4}$

Hence, given statement if FALSE.

Answer 2

Answer:

Option D) is correct

That is the rational exponent expression is not simplified correctly is

$x^{\frac{7}{4}=\sqrt[7]{x^4}$

Step-by-step explanation:

Given rational exponent expression is $x^{\frac{7}{4}=\sqrt[7]{x^4}$

To prove that LHS=RHS

First taking LHS

$x^{\frac{7}{4}$

$=(x^7)^{\frac{1}{4}}$

$=\sqrt[4]{x^7}$

Therefore $x^{\frac{7}{4}=\sqrt[4]{x^7}\neq RHS$

But we have $x^{\frac{7}{4}=\sqrt[7]{x^4}$

Therefore $LHS\neq RHS$

The corrected simplified expression $x^{\frac{7}{4}=\sqrt[4]{x^7}$

Therefore Option D) is correct

Therefore the rational exponent expression which is not simplified correctly is

$x^{\frac{7}{4}=\sqrt[7]{x^4}$