Final answer:
To simplify the expression ((3x⁸)/(2y⁹))³, we raise each term inside the parentheses to the power of 3. The simplified expression is (27x²⁴)/(8y²⁷).
Step-by-step explanation:
To simplify the expression ((3x⁸)/(2y⁹))³, we need to raise each term inside the parentheses to the power of 3. Applying the power of a power rule, we have
((3x⁸)³)/((2y⁹)³). Next, we can simplify each term individually by raising the base and the exponent to the power of 3. For the numerator, we get (3³)(x⁸³) = 27x²⁴, and for the denominator, we get (2³)(y⁹³) = 8y²⁷. Combining these results, we have the simplified expression of (27x²⁴)/(8y²⁷).
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