Advanced MathHardProduct of a square root and a cube root as a single power
Advanced Math practice question
For x > 0, the product √x · ∛x can be written as x^k, where k is a constant. What is the value of k?
Answer: 5/6
√x = x^(1/2) and ∛x = x^(1/3). Multiplying adds the exponents: 1/2 + 1/3 = 5/6.
Common wrong answers
- If you answered 5
- 5 is the numerator of 5/6 alone.
- If you answered 1/6
- 1/6 multiplies the exponents instead of adding them.
- If you answered 1/5
- 1/5 comes from adding the roots' indices (2 + 3) and inverting.
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