1. **State the problem:** Calculate $\left(5.46 \times 10^{-4}\right)^3 + \left(2.23 \times 10^{-5}\right) \times \left(1.39 \times 10^{-6}\right)$ and express the answer in standard form to 3 significant figures. 2. **Recall the rules:** - When raising a number in scientific notation to a power, raise the coefficient to the power and multiply the exponent by that power. - When multiplying numbers in scientific notation, multiply the coefficients and add the exponents. 3. **Calculate the first term:** $$\left(5.46 \times 10^{-4}\right)^3 = 5.46^3 \times 10^{-4 \times 3} = 5.46^3 \times 10^{-12}$$ Calculate $5.46^3$: $$5.46^3 = 5.46 \times 5.46 \times 5.46 = 162.746$$ So, $$\left(5.46 \times 10^{-4}\right)^3 = 162.746 \times 10^{-12}$$ Convert to standard form: $$162.746 \times 10^{-12} = 1.62746 \times 10^{2} \times 10^{-12} = 1.62746 \times 10^{-10}$$ 4. **Calculate the second term:** $$\left(2.23 \times 10^{-5}\right) \times \left(1.39 \times 10^{-6}\right) = (2.23 \times 1.39) \times 10^{-5 + (-6)} = 3.0997 \times 10^{-11}$$ 5. **Add the two terms:** $$1.62746 \times 10^{-10} + 3.0997 \times 10^{-11}$$ Rewrite both with the same exponent: $$1.62746 \times 10^{-10} + 0.30997 \times 10^{-10} = (1.62746 + 0.30997) \times 10^{-10} = 1.93743 \times 10^{-10}$$ 6. **Round to 3 significant figures:** $$1.94 \times 10^{-10}$$ **Final answer:** $$\boxed{1.94 \times 10^{-10}}$$