1) $x^3 = 216$
$x^3 = 6^3$
$x = 6$.

2) $x^2 = 16$
$x^2 = 4^2$
$x = \pm 4$.

3) $x^5 = 243$
$x^5 = 3^5$
$x = 3$.

4) $2x^3 + 1 = 55$
$2x^3 = 55 - 1$
$2x^3 = 54$
$x^3 = 54 \div 2$
$x^3 = 27$
$x^3 = 3^3$
$x = 3$.

5) $7x^2 - 8 = 2^2 \cdot 5$
$7x^2 - 8 = 4 \cdot 5$
$7x^2 - 8 = 20$
$7x^2 = 20 + 8$
$7x^2 = 28$
$x^2 = 28 \div 7$
$x^2 = 4$
$x^2 = 2^2$
$x = \pm 2$.

6) $175 - 3x^3 = 94$
$3x^3 = 175 - 94$
$3x^3 = 81$
$x^3 = 81 \div 3$
$x^3 = 27$
$x^3 = 3^3$
$x = 3$.

7) $(2x-4)^3 = 512$
$(2x-4)^3 = 8^3$
$2x-4 = 8$
$2x = 8 + 4$
$2x = 12$
$x = 12 \div 2$
$x = 6$.

8) $(18-3x)^3 = 216$
$(18-3x)^3 = 6^3$
$18-3x = 6$
$3x = 18 - 6$
$3x = 12$
$x = 12 \div 3$
$x = 4$.

9) $(20-6x)^5 = 32$
$(20-6x)^5 = 2^5$
$20-6x = 2$
$6x = 20 - 2$
$6x = 18$
$x = 18 \div 6$
$x = 3$.

10) $175 - 75 \cdot (x-1)^2 = 10^2$
$175 - 75 \cdot (x-1)^2 = 100$
$75 \cdot (x-1)^2 = 175 - 100$
$75 \cdot (x-1)^2 = 75$
$(x-1)^2 = 75 \div 75$
$(x-1)^2 = 1$
$x-1 = 1$ hoặc $x-1 = -1$.
TH1: $x-1 = 1 \Rightarrow x = 1+1 \Rightarrow x = 2$.
TH2: $x-1 = -1 \Rightarrow x = -1+1 \Rightarrow x = 0$.
Vậy $x = 0$ hoặc $x = 2$.