https://file.aiquickdraw.com/mathbot/file/1727304159623qm8a9bb6.jpg

Let's break down and solve each problem from the image:

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### Question 15:
**Problem:**  
\( \sqrt{12} \times \sqrt{15} \)

**Solution:**  
Use the property of square roots:  
\[
\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}
\]
So,  
\[
\sqrt{12} \times \sqrt{15} = \sqrt{12 \times 15} = \sqrt{180}
\]
We can simplify \( \sqrt{180} \):
\[
180 = 36 \times 5 \implies \sqrt{180} = \sqrt{36 \times 5} = 6\sqrt{5}
\]

Thus, the answer is:  
\[
6\sqrt{5}
\]

---

### Question 16:
**Problem:**  
If \( ^{2}\log 3 = a \) and \( ^{3}\log 5 = b \), find \( ^{6}\log 15 \).

**Solution:**  
We can use the logarithmic rule:
\[
\log(ab) = \log a + \log b
\]
So,  
\[
^{6}\log 15 = ^{6}\log(3 \times 5) = ^{6}\log 3 + ^{6}\log 5
\]
Now, express \( ^{6}\log 3 \) and \( ^{6}\log 5 \) in terms of \( a \) and \( b \):
\[
^{6}\log 3 = \frac{^{2}\log 3}{3} = \frac{a}{3}
\]
\[
^{6}\log 5 = \frac{^{3}\log 5}{2} = \frac{b}{2}
\]

Thus,  
\[
^{6}\log 15 = \frac{a}{3} + \frac{b}{2}
\]
To combine these, find the common denominator:
\[
^{6}\log 15 = \frac{2a}{6} + \frac{3b}{6} = \frac{2a + 3b}{6}
\]

---

### Question 17:
**Problem:**  
Convert the following expression into positive exponents:  
\[
\frac{x^{-2} + y^{-3}}{xy^{-1} + x^{-3}y^2}
\]

**Solution:**  
Let's rewrite each term with positive exponents.

- \( x^{-2} = \frac{1}{x^2} \)
- \( y^{-3} = \frac{1}{y^3} \)
- \( y^{-1} = \frac{1}{y} \)
- \( x^{-3} = \frac{1}{x^3} \)

Now substitute these into the expression:
\[
\frac{\frac{1}{x^2} + \frac{1}{y^3}}{x \cdot \frac{1}{y} + \frac{1}{x^3} \cdot y^2}
\]
Simplify the terms inside the denominator:
\[
x \cdot \frac{1}{y} = \frac{x}{y}, \quad \frac{1}{x^3} \cdot y^2 = \frac{y^2}{x^3}
\]
So, the expression becomes:
\[
\frac{\frac{1}{x^2} + \frac{1}{y^3}}{\frac{x}{y} + \frac{y^2}{x^3}}
\]
This is the simplified form of the expression with positive exponents.

---

Let me know if you'd like more details or have any questions!

Here are 5 related questions for further practice:
1. Simplify \( \sqrt{8} \times \sqrt{18} \).
2. If \( ^{3}\log 2 = c \), what is \( ^{9}\log 4 \)?
3. Simplify \( \frac{a^{-1} + b^{-1}}{ab^{-1} + a^{-2}b} \).
4. Rewrite \( x^{-3}y^4z^{-2} \) with positive exponents.
5. Solve \( ^{4}\log 80 \) given \( ^{2}\log 5 = a \) and \( ^{3}\log 2 = b \).

**Tip:**  
When working with exponents, remember to apply the laws of exponents consistently to avoid mistakes in simplification!

15. Hasil dari √12 × √15 adalah ...
16. Jika ²log 3 = a dan ³log 5 = b, ⁶log 15 adalah ...
17. Ubahlah (x⁻² + y⁻³) / (xy⁻¹ + x⁻³y²) ke dalam bentuk pangkat positif!

This page explains how to simplify expressions involving radicals (√12 × √15), logarithmic transformations (logarithmic properties with base changes), and converting negative exponents to positive ones. Suitable for students in Grades 10-12, this guide provides step-by-step solutions to these math problems.

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