we have
[tex]((\sqrt[5]{x})^{7})^{3}[/tex]
[tex]((\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}[/tex]
therefore
the answer is
[tex]x^{4} \sqrt[5]{x}[/tex]
Answer:
Hence, the transformation of the given quantity into an expression with a rational exponent is:
[tex]x^{\dfrac{21}{5}}[/tex]
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:
[tex](\sqrt[5]{x}^7)^3[/tex]
i.e. the expression could also be written as:
[tex]=(x^{\dfrac{7}{5})^3[/tex]
( since,
[tex](x^{\frac{1}{n})^m=x^{\frac{m}{n}}[/tex]
which is further represented as:
[tex]x^{\dfrac{21}{5}}[/tex]
( Since, we have:
[tex](x^m)^n=x^{mn}[/tex]
Hence, the expression is:
[tex]x^{\dfrac{21}{5}}[/tex]
