$\text{a)}{7}^x=\sqrt[3]{7}$  

$7^x=7^{\frac{1}{3}}$  

$x=\frac{1}{3}$  

---

$\text{b)}{3}^x=\sqrt[4]{27}$  

$3^x=\sqrt[4]{3^3}$  

$3^x=3^{\frac{3}{4}}$  

$x=\frac{3}{4}$  

---

$\text{c)}{4}^x=\frac{\sqrt[3]{4}}{8}$  

${\left(2^2\right)}^x=\frac{2^{\frac{2}{3}}}{2^3}$  

$2^{2x}=2^{-2\frac{1}{3}}$  

$2x=-\frac{7}{3}\mid \cdot \frac{1}{2}$  

$x=-\frac{7}{6}$  

---

$\text{d)}{2}^x=\frac{1}{8}$  

$2^x=\frac{1}{2^3}$  

$2^x=2^{-3}$  

$x=-3$  

---

$\text{e)}{6}^x=\frac{1}{\sqrt[5]{36}}$  

$6^x=\frac{1}{\sqrt[5]{6^2}}$  

$6^x=6^{-\frac{2}{5}}$  

$x=-\frac{2}{5}$  

---

$\text{f)}{125}^x=\frac{25}{\sqrt{5}}$  

${\left(5^3\right)}^x=\frac{5^2}{5^{\frac{1}{2}}}$  

$5^{3x}=5^{1\frac{1}{2}}$  

$3x=\frac{3}{2}\mid \cdot \frac{1}{3}$  

$x=\frac{1}{2}$  

---

$\text{g)}{5}^x=\frac{1}{\sqrt[4]{5}}$  

$5^x=\frac{1}{5^{\frac{1}{4}}}$  

$5^x=5^{-\frac{1}{4}}$  

$x=-\frac{1}{4}$  

---

$\text{h)}{7}^x=49\sqrt{7}$  

$7^x=7^2\cdot 7^{\frac{1}{2}}$  

$7^x=7^{2\frac{1}{2}}$  

$x=2\frac{1}{2}$  

---

$\text{i)}{\left(\sqrt{7}\right)}^x=7\sqrt[3]{7}$  

${\left(7^{\frac{1}{2}}\right)}^x=7^1\cdot 7^{\frac{1}{3}}$  

$7^{\frac{1}{2}x}=7^{1\frac{1}{3}}$  

$\frac{1}{2}x=\frac{4}{3}\mid \cdot 2$  

$x=\frac{8}{3}$  

---

$\text{j)}{9}^x=\sqrt[4]{243}$  

${\left(3^2\right)}^x=\sqrt[4]{3^5}$  

$3^{2x}=3^{\frac{5}{4}}$  

$2x=\frac{5}{4}\mid \cdot \frac{1}{2}$  

$x=\frac{5}{8}$  

---

$\text{k)}{5}^x=\frac{\sqrt[3]{5}}{125}$  

$5^x=\frac{5^{\frac{1}{3}}}{5^3}$  

$5^x=5^{-2\frac{2}{3}}$  

$x=-2\frac{2}{3}$  

---

$\text{l)}{\left(\frac{1}{81}\right)}^x=27\sqrt{3}$  

${\left(3^{-4}\right)}^x=3^3\cdot 3^{\frac{1}{2}}$  

$3^{-4x}=3^{3\frac{1}{2}}$  

$-4x=\frac{7}{2}\mid \cdot \left(-\frac{1}{4}\right)$  

$x=-\frac{7}{8}$