Question

Multiplying fractional exponents? (Equation in the comments)

Answer 1

The equation can also be written on this form:
(x)^(1/3) * (7x)^(1/5)

Answer 2

I know this much, but the options for the answer are in radical form...

Answer 3

What if you try to rewrite one of the two factors so that they fit under eachother, have you tried that? :)

Answer 4

\[x^{1/3}(7x)^{1/5}=x^{1/3}x^{1/5}7^{1/5}\] you add the exponents of factors with the same base. In this case "x" is the base.

Answer 5

\[\sqrt[15]{7x}\] I keep getting that, but it's not one of the options.

Answer 6

Moreover, you're able to rewrite x^(1/3)*x^(1/5) as x^(5/15)*x^(3/15) --> 7^(1/5)*x^(8/15)

Answer 7

If you open the file, you'll be able to see the original problem and available options. I put the answer as \[\sqrt[15]{7x^{8}}\]

Answer 8

Hmm, If you want to rewrite 7^(1/5) as 7^(1/15) you need to extend the exponent quotient with 3 --> 7^(3/15) --> (7^3)^(1/15) --> (343)^(1/15) Therefore C would actually be the correct answer.

Answer 9

Tricky one, I almost fell! :D

Answer 10

\[x^{1/3}x^{1/5}\] is \[ x^{1/3+1/5}\]. Now \[1/3+1/5=5/15+3/15=8/15\] that gives us \[x^{1/3+1/5}=x^{8/15} \] this result is multiplied by \[ 7^{1/5}=7^{3/15}=(7^3)^{1/15} \] so your answer would be \[ (7^{3}x^8)^{1/15} \]