Question

Describe how to transform the quantity of the fifth root of x to the seventh power, to the third powerinto an expression with a rational exponent. Make sure you respond with complete sentences.

Answer 1

Answer:

Hence, the transformation of the given quantity into an expression with a rational exponent is:

$x^{\dfrac{21}{5}}$

Step-by-step explanation:

We are given an algebraic quantity as:

fifth root of x to the seventh power, to the third power into an expression with a rational exponent.

i.e. we have to convert the given algebraic quantity:

$(\sqrt[5]{x}^7)^3$

i.e. the expression could also be written as:

$=(x^{\dfrac{7}{5})^3$

( since,

$(x^{\frac{1}{n})^m=x^{\frac{m}{n}}$

which is further represented as:

$x^{\dfrac{21}{5}}$

( Since, we have:

$(x^m)^n=x^{mn}$

Hence, the expression is:

$x^{\dfrac{21}{5}}$

Answer 2

we have

$((\sqrt[5]{x})^{7})^{3}$

$((\sqrt[5]{x}})^{7})^{3}=((x^{\frac{1}{5}})^{7})^{3}\\\\ \\=( x^{\frac{1*7}{5}})^{3}\\ \\=x^{\frac{21}{5}}\\ \\= \sqrt[5]{x^{21}} \\ \\=\sqrt[5]{x^{5}x^{5}x^{5}x^{5}x} \\ \\=x^{4} \sqrt[5]{x}$

therefore

the answer is

$x^{4} \sqrt[5]{x}$