How do you multiply #3^ { \frac { 2} { 5} } \cdot x ^ { \frac { 1} { 5} }#?

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Answer 1 · 2017-07-19T14:35:28

See a solution process below:

First, rewrite the expression as:

#3^(2 xx 1/5) * x^(1/5)#

We can now use this rule of exponents to rewrite the #3# term:

#x^(color(red)(a) xx color(blue)(b)) = (x^color(red)(a))^color(blue)(b)#

#3^(2 xx 1/5) * x^(1/5) => (3^2)^(1/5) * x^(1/5) => 9^(1/5) * x^(1/5)#

Now, we can use this rule for exponents to rewrite the expression:

#color(red)(a)^x xx color(blue)(b)^x = (color(red)(a) xx color(blue)(b))^x#

#9^(1/5) * x^(1/5) => (9 * x)^(1/5) => (9x)^(1/5)#

Or, in radical form:

#root(5)(9x)#