Question

(0,064^2/3*16^1/6)^3/2

Answer 1

0,064^2/3=0,4^2

16^1/6)^3/2=2^4*1\6*3\2=2

0,4^2*3/2=0,4^3

0,064*2=0,128

Answer 2

Let's simplify the expression step by step:

Step 1: Calculate the exponents first.

• $0.064^{2/3} = (0.064)^{0.666...}$ (The exponent $2/3$ is equivalent to $0.666...$ as a repeating decimal.)
• $16^{1/6} = 16^{0.166...}$ (The exponent $1/6$ is equivalent to $0.166...$ as a repeating decimal.)

Step 2: Raise the exponents to the power of 3. $(0.064^{2/3})^3 = (0.064)^{0.666... \times 3} = (0.064)^2$ $(16^{1/6})^3 = 16^{0.166... \times 3} = 16^{0.5} = 4$

Step 3: Take the square root of the product of the two results from Step 2. $\sqrt{(0.064^{2/3})^3 \times (16^{1/6})^3} = \sqrt{(0.064)^2 \times 4} = \sqrt{0.004096 \times 4} = \sqrt{0.016384} \approx 0.128$

So, the value of the expression is approximately 0.128.