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

@AllTehMaffs do you know how to do this one?

Answer 2

Is that exactly how the question is written? ... hmm...

Answer 3

\(\bf \textit{keep in mind that}\qquad \huge \sqrt[m]{a^n}=a^{\frac{n}{m}}\)

Answer 4

\(\huge \sqrt[5]{x^{7^3}}\implies \sqrt[5]{x^{49}}\implies \square ?\)

Answer 5

woops

Answer 6

OH, I get it. Was reading it wrong.

So our original expression is

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

and
\[ (x^{a})^b = x^{ab}\]

Use that, and then also what jdoe wrote :)

Answer 7

\(\huge \sqrt[5]{x^{7^3}}\implies \sqrt[5]{x^{343}}\implies \square ?\)

Answer 8

wel.... dunno.. is it \(\huge \sqrt[5]{x^{7^3}}\qquad or\qquad \sqrt[5]{(x^7)^3}\quad ?\)

Answer 9

well @jdoe0001 .... the equation is in parenthesis and the ^3 is on the outside

Answer 10

then
\[ (x^7)^3 = x^{21} \]
slightly more manageable :)

Answer 11

\(\huge{ \sqrt[5]{(x^7)^3}\implies \sqrt[5]{x^{7\cdot 3}}\\ \quad \\
\textit{keep in mind that }\quad a^{\frac{n}{m}} = \sqrt[m]{a^n}}\)

Answer 12

thanks so much! :) @AllTehMaffs @jdoe0001