Question

Describe how to transform d="TexFormula1" title="( \sqrt[3]{x} ^ {4} ) ^{5} " alt="( \sqrt[3]{x} ^ {4} ) ^{5} " align="absmiddle" class="latex-formula"> into an expression with a rational exponent. Make sure you respond with complete sentences.

Answer 1

Well the rule for bases with multiple exponents is:

((a^b)^c)^d = a^(b*c*d)

So in this case we have:

(((x^(1/3))^4)^5

x^(4*5*1/3)

x^(20/3)

The "transformation" for a base being raised to multiple exponents is to raise the base to the power of the product of all exponents.