Step 1: Rewrite the base on the left side of the equation so it matches the base on the right side. The equation is given as: $$(1/4)^x = 2^{3x-3}$$ We know that $1/4$ can be written as $2^{-2}$. Step 2: Substitute $2^{-2}$ for $1/4$ in the equation. $$(2^{-2})^x = 2^{3x-3}$$ Step 3: Apply the exponent rule $(a^m)^n = a^{mn}$ to the left side. $$2^{-2x} = 2^{3x-3}$$ Step 4: Since the bases are now the same, equate the exponents. $$-2x = 3x-3$$ Step 5: Solve the linear equation for $x$. Add $2x$ to both sides of the equation: $$0 = 3x + 2x - 3$$ $$0 = 5x - 3$$ Add 3 to both sides: $$3 = 5x$$ Divide by 5: $$x = \frac{3}{5}$$ The value of $x$ is $\frac{3}{5}$. $$\boxed{x = \frac{3}{5}}$$ Send me the next one 📸