Question

How do I do solve the problem in the picture

Answer 1

Explanation:

by knowing how square roots, divisions and multiplications impact exponents.

x^(a/b) means

`\sqrt[b]{ {x}^(a) }`

x^a × x^b = x^(a+b)

x^a / x^b = x^(a-b)

x^(-a) = 1/x^a

so, now that we know all that, we can attack our actual problem :

`\sqrt[8]{ {x}^(7) } / \sqrt[16]{ {x}^(3) }`

this means we have

x^(7/8) / x^(3/16) = x^(7/8 - 3/16)

you remember how to compare and add or subtract fractions ? we need to bring them to the same denominator.

here we have 8th and 16th.

so, we need to bring the 8th to 16th.

how many 16th are in a whole compared to 8th ? twice as many, of course (as 8×2 = 16).

so, 7/8 = 7/8 × 2/2 = 14/16.

remember, we always need to multiply numerator and denominator with the same factor to keep the value of the fraction unchanged.

and so, we actually have

x^(7/8) / x^(3/16) = x^(7/8 - 3/16) = x^(14/16 - 3/16) =

= x^(11/16) =

=

`\sqrt[16]{ {x}^(11) }`

since we don't know any further information about x, we cannot solve this in the sense of calculating a resulting number.

we can only simplify the expression. which we did.