Question

Please help I need to finish my winter packet and no one is answering my questions

Answer 1

Answer:

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

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

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

Step-by-step explanation:

we have

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

Remember the properties

$\sqrt[n]{a^{m}}=a^{\frac{m}{n}}$

$(a^m)^{n}=a^{m*n}$

so

Verify each case

Part 1) we have

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

we know that

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

Compare with the given expression

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

Part 2) we have

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

we know that

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

Compare with the given expression

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

therefore

Is equivalent to the given expression

Part 3) we have

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

we know that

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

Compare with the given expression

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

therefore

Is equivalent to the given expression

Part 4) we have

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

we know that

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

Compare with the given expression

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

Part 5) we have

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

we know that

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

Compare with the given expression

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

Part 6) we have

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

we know that

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

Compare with the given expression

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

therefore

Is equivalent to the given expression