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Step 1:I'll solve this step by step using the precise LaTeX formatting guidelines you specified:
Step 2:: Identify the Exponent Rule
The rule is: $$(x^{a})^{b} = x^{ab}
When raising a power to another power, we multiply the exponents.
Step 3:: Apply the Exponent Rule to the Given Expression
For $$(x^{6})^{3}$$, we multiply the exponents:
x^{6 \times 3} = x^{18}
Step 4:: Verify the Calculation
- Multiplying exponents: $$6 \times 3 = 18
- Original inner exponent: 6
Final Answer
Key Insights: - When raising a power to another power, multiply the exponents - The base remains unchanged - This rule applies to any base and any exponents
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