Question

How would i simplify this?

Answer 1

rewrite the root as a (fractional) exponent
do you know how to do that ?

Answer 2

i dont think so...
how would i do that?

Answer 3

use the rule
\[ \sqrt[n]{x} = x^\frac{1}{n} \]

Answer 4

that rule says "look for the little number in front of the root sign"
what is the number in your problem ?

Answer 5

7?

Answer 6

yes. the little number is 7
the rule says write x with the exponent 1/7
can you do that ?

Answer 7

so it would just be x1/7? what happens to the 21?

Answer 8

we do these problems in steps
so far, we have
\[ \sqrt[7]{x}= x^{\frac{1}{7} }\]
we use that to rewrite your problem as
\[ \left( \sqrt[7]{x}\right)^{21} = \left( x^{\frac{1}{7} }\right)^{21} \]

Answer 9

now we use another rule about exponents
\[ \left(x^a \right)^b = x^{ab} \]
that rule says if you make b the exponent of (x^a) that is the same as
x to the exponent a*b (a times b)

in other words, you multiply 1/7 * 21 to get a new exponent to replace both the 1/7 and the 21