Question

Which expression is equivalent to RootIndex 4 StartRoot x Superscript 10 Baseline EndRoot? x squared (RootIndex 4 StartRoot x squared EndRoot) x2.2 x cubed (RootIndex 4 StartRoot x EndRoot) x5

Answer 1

Answer:

The option x squared ( root index 4 start root x squared end root) is correct

Therefore the equivalent expression to the given expression is $x^2\sqrt[4]{x^2}$

Step-by-step explanation:

Given expression is $\sqrt[4]{x^{10}}$

To find the equivalent expression to the given expression :

$\sqrt[4]{x^{10}}$

$=\sqrt[4]{x^{8+2}}$

$=\sqrt[4]{x^8.x^2}$ ( using the property $a^m.a^n=a^{m+n}$ )

$=\sqrt[4]{x^{2\times 4}.x^2}$

$=\sqrt[4]{(x^2)^4x^2}$ ( using the peoperty $a^{mn}=(a^m)^n$ )

$=\sqrt[4]{(x^2)^4}\times \sqrt[4]{x^2}$ ( using the property $\sqrt{ab}=\sqrt{a}\times \sqrt{b}$ )

$=x^2\sqrt[4]{x^2}$

Therefore $\sqrt[4]{x^{10}}=x^2\sqrt[4]{x^2}$

Therefore the equivalent expression to the given expression is $x^2\sqrt[4]{x^2}$

The option "x squared (RootIndex 4 StartRoot x squared EndRoot)" is correct

That is $x^2\sqrt[4]{x^2}$ is correct

Answer 2

Answer:

the correct answer is A

Step-by-step explanation:

hope this helped