1. **Problem statement:** Simplify the expression $\left(V^3 V^{-1.5} V^2\right)^2$ using the laws of indices. 2. **Recall the laws of indices:** - When multiplying powers with the same base, add the exponents: $a^m \times a^n = a^{m+n}$. - When raising a power to another power, multiply the exponents: $\left(a^m\right)^n = a^{m \times n}$. 3. **Simplify inside the parentheses first:** $$V^3 \times V^{-1.5} \times V^2 = V^{3 + (-1.5) + 2} = V^{3 - 1.5 + 2} = V^{3.5}$$ 4. **Now raise the result to the power 2:** $$\left(V^{3.5}\right)^2 = V^{3.5 \times 2} = V^7$$ 5. **Final answer:** $$V^7$$ This means the simplified form of the expression is $V^7$.