Question

Simplify open parentheses x to the 2 fifths power close parentheses to the 5 sixths power.

A) x to the 37 over 30 power
B) x to the 13 over 30 power
C) x to the 10 elevenths power
D) x to the 1 third power

Answer 1

The correct answer option is D) x to the 1 third power.

Explanation:

Firstly, we will translate the given word expression (open parentheses x to the 2 fifths power close parentheses to the 5 sixths power) into mathematical expression:

`(x^{(2)/(5) })^{(5)/(6)`

Now to simplify this, we must recall the law of multiplying the powers:

`(a^m)^n=a^(mn)`

So for the given expression, we will multiply the powers to get:

=
`x^{(2)/(5) }*^{(5)/(6)`

=
`(x^{(2)/(6) })`

=
`(x^{(1)/(3) })`

Therefore, the correct answer option is D) x to the 1 third power.

Answer 2

D.
`x^{(1)/(3) }`

Explanation:

`(x^{(2)/(5) } )^{(5)/(6) }`

Applying law of exponents
`(x^(m))^(n) = x^(m*n)`, we have

`x^{(2)/(5) *(5)/(6) }`

=
`x^{(10)/(30) }`

Simplifying
`{(10)/(30) }` we get
`{(1)/(3) }`

So, the final answer is
`x^{(1)/(3) }`