Question 187
a) Let $a \gt 0$ and $b \gt 0$. Simplify the expression
$$
7\left(\frac{a^{5}}{2 b^{4}}\right)^{5} \cdot \left(\frac{2 b^{2}}{a^{4}}\right)^{5} - 3\left(\frac{a}{b^{2}}\right)^{3+2x} \cdot \left(\frac{a^{2}}{b^{4}}\right)^{1-x} + \left(4 a^{5} b\right)^{5} : \left(2 a^{4} b^{3}\right)^{5}
$$
b) Compute the value of the expression for $a = 5^{\frac{1}{5}}$ and $b = \sqrt[5]{2}$.
$$
7\left(\frac{a^{5}}{2 b^{4}}\right)^{5} \cdot \left(\frac{2 b^{2}}{a^{4}}\right)^{5} - 3\left(\frac{a}{b^{2}}\right)^{3+2x} \cdot \left(\frac{a^{2}}{b^{4}}\right)^{1-x} + \left(4 a^{5} b\right)^{5} : \left(2 a^{4} b^{3}\right)^{5}
$$
b) Compute the value of the expression for $a = 5^{\frac{1}{5}}$ and $b = \sqrt[5]{2}$.