Question

Rewrite the expression in the form k times x^n

Answer 1

`\mathbf{Task.} ~ \mathrm{Rewrite~the~expression~in~the~form~} k \cdot x^(n).`

`First~way\colon`

`\left(16\sqrt{x^(3)} \right)^{\tfrac{1}{4} }= \left(2^(4)\cdot x^{\tfrac{3}{2} } \right)^\bigg{(1)/(4) } = 2^{4 \cdot \tfrac{1}{4} } \cdot x^{\tfrac{3}{2} \cdot \tfrac{1}{4} } = 2 \cdot x^{\tfrac{3}{8} }`

`Second~way\colon`

`\left(16\sqrt{x^(3)} \right)^{\tfrac{1}{4} }= \sqrt[4]{16 \cdot \sqrt{x^(3)}} = \sqrt[4]{2^(4)} \cdot \sqrt[4]{\sqrt{x^(3)}} = 2 \cdot \sqrt[8]{x^(3)} = 2 \cdot x^{\tfrac{3}{8} }`

`Answer\colon~2 \cdot x^{\tfrac{3}{8} }. ~ \blacktriangle`