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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.