Question

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

Answer 1

\[ \left( \sqrt[6]{x^{5}} \right) ^7 \]

there are 2 ways to work this out

the way we want it to be is like this: \( \sqrt[n]{x^b}=a^{\frac{b}{n}} \Rightarrow x^{ \frac{5}{6} \times \frac{7}{1} } \Rightarrow x^ {\frac{35}{6}} \)

you work the "respond with complete sentences"



we could also do it the 2nd way, which is the same thing, just that we do the b transformation part in a diff way:

firstly we convert the sixth root to a power whose form is "\( \frac{1}{6} \)" \( \Rightarrow \left[ \left(x^{5}\right)^{\frac{1}{6}}\right] ^{7} \)

we can finish it off, by multiplying the exponents
\[ \frac{5}{1} \times \frac{1}{6} \times \frac{7}{1} = \frac{35}{6}\]
thus, we get :

\( \left[ \left(x^{5}\right)^{\frac{1}{6}}\right] ^{7} \Rightarrow x^ {\frac{35}{6}} \)

Answer 2

thank you,,i was literally hopin for help

Answer 3

lol why did u close it then