Simplify the expression with rational exponents: (16x^4 / y^8)^(3/4) for positive x and y.
Answer and explanation
Correct answer: B. 8x^3 / y^6
- Step 1: Apply exponent to 16: 16^(3/4) = (16^(1/4))^3 = 2^3 = 8. Step 2. Apply exponent to variables: (x^4)^(3/4) = x^3 and (y^8)^(3/4) = y^6. Step 3. Combine: 8x^3 / y^6. Answer: 8x^3 / y^6. Why not the others: 12 multiplies 16 by 3/4 instead of raising to the power; y^8 ignores the power on the denominator; 16 forgets to evaluate 16^(3/4).
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