1. **State the problem:** Simplify the expression $$(4^2 \times 4^3)^2 - (5^4 \div 5^2)^2$$ 2. **Use exponent rules:** - When multiplying powers with the same base, add exponents: $a^m \times a^n = a^{m+n}$. - When raising a power to another power, multiply exponents: $(a^m)^n = a^{m \times n}$. - When dividing powers with the same base, subtract exponents: $\frac{a^m}{a^n} = a^{m-n}$. 3. **Simplify each part:** - For $(4^2 \times 4^3)^2$, first add exponents inside the parentheses: $4^{2+3} = 4^5$. - Then raise to the power 2: $(4^5)^2 = 4^{5 \times 2} = 4^{10}$. - For $(5^4 \div 5^2)^2$, subtract exponents inside the parentheses: $5^{4-2} = 5^2$. - Then raise to the power 2: $(5^2)^2 = 5^{2 \times 2} = 5^4$. 4. **Rewrite the expression:** $$4^{10} - 5^4$$ 5. **Calculate the values:** - $4^{10} = 1048576$ - $5^4 = 625$ 6. **Subtract:** $$1048576 - 625 = 1047951$$ **Final answer:** $1047951$