Megan:
x to the one third power =

<span>x to the one twelfth power = </span>

<span>The quantity of x to the one third power, over x to the one twelfth power is:
</span>

<span>
Since </span>

then

Now, just subtract exponents:
1/3 - 1/12 = 4/12 - 1/12 = 3/12 = 1/4

Julie:
x times x to the second times x to the fifth = x * x² * x⁵
<span>The thirty second root of the quantity of x times x to the second times x to the fifth is
</span>
![\sqrt[32]{x* x^{2} * x^{5} }](https://tex.z-dn.net/?f=%20%5Csqrt%5B32%5D%7Bx%2A%20x%5E%7B2%7D%20%2A%20x%5E%7B5%7D%20%7D%20)
<span>
Since </span>

Then
![\sqrt[32]{x* x^{2} * x^{5} }= \sqrt[32]{ x^{1+2+5} } =\sqrt[32]{ x^{8} }](https://tex.z-dn.net/?f=%5Csqrt%5B32%5D%7Bx%2A%20x%5E%7B2%7D%20%2A%20x%5E%7B5%7D%20%7D%3D%20%5Csqrt%5B32%5D%7B%20x%5E%7B1%2B2%2B5%7D%20%7D%20%3D%5Csqrt%5B32%5D%7B%20x%5E%7B8%7D%20%7D)
Since
![\sqrt[n]{x^{m}} = x^{m/n} }](https://tex.z-dn.net/?f=%20%5Csqrt%5Bn%5D%7Bx%5E%7Bm%7D%7D%20%3D%20x%5E%7Bm%2Fn%7D%20%7D%20)
Then
![\sqrt[32]{ x^{8} }= x^{8/32} = x^{1/4}](https://tex.z-dn.net/?f=%5Csqrt%5B32%5D%7B%20x%5E%7B8%7D%20%7D%3D%20x%5E%7B8%2F32%7D%20%3D%20x%5E%7B1%2F4%7D%20)
Since both Megan and Julie got the same result, it can be concluded that their expressions are equivalent.
Answer:
13)
⇒
15)
⇒
Step-by-step explanation:
Given expression:
13) 
15) 
Write the expressions in radical form.
Solution:
For an expression with exponents as fraction like

the numerator
represents the power it is raised to and the denominator
represents the nth root of the expression.
For an expression with exponents as negative fraction like

We take the reciprocal of the term by rule for negative exponents.
So it is written as:

using the above properties we can write the given expressions in radical form.
13) 
⇒
[Using rule of negative exponents]
⇒
[writing in radical form]
15) 
⇒
[Since 2nd root is given as
in radical form]
The percentage of the scores that are between 75.8 and 89 is; 95%
<h3>How to find the percentage from z-score?</h3>
We are given;
Population mean; μ
Standard deviation; σ = 3.3
Thus;
z-score for a mean score of 75.8 is;
z = (75.8 - 82.4)/3.3
z = -2
z-score for a mean score of 89 is;
z = (89 - 82.4)/3.3
z = 2
From online p-value from z-score calculator, the p-value between both z-scores is;
p-value = 0.9545 = 95.45%
Approximating to the nearest percent = 95%
Read more about z-score at; brainly.com/question/25638875
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