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I see that you've uploaded a photo of a mathematical worksheet covering topics like exponents, roots, and logarithms. I'll help solve some of the problems step-by-step.

### Section: **Pangkat & Akar (Exponents & Roots)**

1. \( 2 \cdot (3^{-1}) \)
   \[
   = 2 \cdot \frac{1}{3} = \frac{2}{3}
   \]

2. \( (2^3)^4 \cdot (2^3)^{-5} \)
   Use the power rule for exponents: \( (a^m)^n = a^{m \cdot n} \).
   \[
   (2^3)^4 = 2^{12}, \quad (2^3)^{-5} = 2^{-15}
   \]
   Now combine the exponents:
   \[
   2^{12} \cdot 2^{-15} = 2^{12 - 15} = 2^{-3} = \frac{1}{2^3} = \frac{1}{8}
   \]

3. \( 3 \cdot 3^{10} \div 3^5 \)
   Using the exponent division rule: \( \frac{a^m}{a^n} = a^{m-n} \),
   \[
   3 \cdot 3^{10 - 5} = 3 \cdot 3^5 = 3^6 = 729
   \]

4. If \( 3^{2x} = 45 \), find \( 3^x \).
   First express 45 as a power of 3.
   \[
   3^{2x} = 45 \implies 2x = \log_3 45
   \]
   Approximation gives \( 3^x \approx 6.7 \) (as solving requires logarithms).

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### Related Questions
1. How do you solve exponential equations with unknown exponents?
2. What is the general rule for simplifying exponent expressions like \( (a^m)^n \)?
3. How can logarithms be used to solve \( a^x = b \)?
4. How are logarithms of roots and powers calculated?
5. What are the differences between natural logarithms and base-10 logarithms?

### Tip
Always combine exponents by adding or subtracting them when you multiply or divide terms with the same base.

Mathematical worksheet involving exponents, roots, and logarithms.

This worksheet covers problems related to exponents, square roots, and logarithmic equations. Learn how to simplify and solve mathematical expressions involving powers and logarithms step-by-step. Suitable for high school students in grades 9-12.

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