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:
\(x^{\dfrac{21}{5}}\)
