Question

(2/3ab^2)^3∙3/2a^3b^2

Answer 1

=(8/27a³b⁶×3)/2a³b²=(8/9b⁴)/2=4b⁴/9

Answer 2

To simplify the expression $(2/3ab^2)^3 \cdot 3/2a^3b^2$, you can follow these steps:

Step 1: Cube the expression inside the parentheses: $(2/3ab^2)^3 = (2/3ab^2) \cdot (2/3ab^2) \cdot (2/3ab^2)$

Now, we have: $(2/3ab^2)^3 = (8/27a^3b^6)$

Step 2: Multiply the result from Step 1 by $3/2a^3b^2$: $(8/27a^3b^6) \cdot (3/2a^3b^2)$

Step 3: Multiply the numerators and denominators separately: Numerator: $8 \cdot 3 = 24$ Denominator: $27 \cdot 2 = 54$

So, the simplified expression is: $\frac{24}{54a^3b^6}$

Step 4: Reduce the fraction by dividing both the numerator and denominator by their greatest common factor, which is 6: $\frac{24/6}{54/6a^3b^6} = \frac{4}{9a^3b^6}$

The final simplified expression is $\frac{4}{9a^3b^6}$.