1. **State the problem:** Simplify the expression $$\frac{(e'f^3 g)^{-3}}{10 e^0 f g^{-4}}$$ where the numerator and denominator are enclosed in curved brackets. 2. **Recall exponent rules:** - $a^0 = 1$ for any $a \neq 0$. - $(abc)^n = a^n b^n c^n$. - $a^{-n} = \frac{1}{a^n}$. - When dividing like bases, subtract exponents: $\frac{a^m}{a^n} = a^{m-n}$. 3. **Rewrite numerator:** $$(e'f^3 g)^{-3} = (e')^{-3} (f^3)^{-3} g^{-3} = e'^{-3} f^{-9} g^{-3}$$ 4. **Rewrite denominator:** $$10 e^0 f g^{-4} = 10 \times 1 \times f^1 \times g^{-4} = 10 f g^{-4}$$ 5. **Form the fraction:** $$\frac{e'^{-3} f^{-9} g^{-3}}{10 f g^{-4}}$$ 6. **Divide like bases by subtracting exponents:** - For $f$: $f^{-9} / f^{1} = f^{-9-1} = f^{-10}$ - For $g$: $g^{-3} / g^{-4} = g^{-3 - (-4)} = g^{1}$ 7. **Simplify the fraction:** $$\frac{e'^{-3} f^{-10} g^{1}}{10} = \frac{g e'^{-3} f^{-10}}{10}$$ 8. **Rewrite negative exponents as positive in denominator:** $$= \frac{g}{10 e'^3 f^{10}}$$ **Final answer:** $$\boxed{\frac{g}{10 e'^3 f^{10}}}$$