Power Expression 6Aa06C

1. **State the problem:** Simplify the expression $$\left(3w^3 \times w^4\right)^3$$. 2. **Recall the rules:** - When multiplying powers with the same base, add the exponents: $$a^m \times a^n = a^{m+n}$$. - When raising a power to another power, multiply the exponents: $$(a^m)^n = a^{m \times n}$$. 3. **Simplify inside the parentheses:** $$3w^3 \times w^4 = 3w^{3+4} = 3w^7$$ 4. **Raise the entire expression to the power of 3:** $$\left(3w^7\right)^3 = 3^3 \times \left(w^7\right)^3$$ 5. **Calculate powers:** $$3^3 = 27$$ $$\left(w^7\right)^3 = w^{7 \times 3} = w^{21}$$ 6. **Final simplified expression:** $$27w^{21}$$