https://file.aiquickdraw.com/mathbot/file/1726711200752qqwz5mp0.jpg

Let's go through each question one by one.

### Question 1
Given the expression:
\[
\frac{8pq}{2^5 p^{-2} r} \cdot (pr)^3
\]

First, simplify the fraction:
\[
\frac{8pq}{2^5 p^{-2} r} = \frac{8pq}{32 p^{-2} r} = \frac{8}{32} \cdot \frac{pq}{p^{-2} r}
\]
\[
= \frac{1}{4} \cdot \frac{pq}{p^{-2} r} = \frac{1}{4} \cdot p^{1-(-2)} \cdot \frac{q}{r} = \frac{1}{4} p^{3} \frac{q}{r}
\]

Now, multiply by \((pr)^3\):
\[
\frac{1}{4} p^3 \frac{q}{r} \cdot p^3 r^3 = \frac{1}{4} p^{3+3} q r^{3-1} = \frac{1}{4} p^6 q r^2
\]

The simplified form is \(\frac{1}{4} p^6 q r^2\).

So, the answer is:
**A. \(\frac{1}{4} p^6 q r^2\)**

### Question 2
Given \(x = 8\) and \(y = 25\), find the value of:
\[
\frac{x^{\frac{2}{3}} \sqrt{y}}{x^{\frac{2}{3}} + y^{-\frac{1}{2}}}
\]

1. Calculate \(x^{\frac{2}{3}}\):
\[
x^{\frac{2}{3}} = 8^{\frac{2}{3}} = (2^3)^{\frac{2}{3}} = 2^{3 \cdot \frac{2}{3}} = 2^2 = 4
\]

2. Calculate \(\sqrt{y}\):
\[
\sqrt{y} = \sqrt{25} = 5
\]

3. Calculate \(y^{-\frac{1}{2}}\):
\[
y^{-\frac{1}{2}} = \frac{1}{\sqrt{25}} = \frac{1}{5}
\]

4. Substitute the values into the expression:
\[
\frac{4 \cdot 5}{4 + \frac{1}{5}} = \frac{20}{\frac{20}{5} + \frac{1}{5}} = \frac{20}{\frac{21}{5}} = 20 \cdot \frac{5}{21} = \frac{100}{21}
\]

So, the answer is:
**

1. Bentuk sederhana dari (8pq) / (2^5 p^(-2) r) . (pr)^3
2. Jika x = 8 dan y = 25, nilai (x^(2/3) sqrt(y)) / (x^(2/3) + y^(-1/2)) adalah?

Learn how to simplify algebraic expressions involving exponents and fractions, and solve the given expression when x = 8 and y = 25. This step-by-step solution covers key algebraic concepts, exponentiation rules, and radical expressions, suitable for Grades 9-10 students.

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