1. **State the problem:** Simplify the expression $$\left(5^8 \cdot 5^4 \cdot 5 \div 5^{11}\right) \cdot 3^0 - \left(15^6 \cdot 15 \div 15^3\right) \div \left(\frac{30}{2}\right)^3$$. 2. **Recall exponent rules:** - When multiplying powers with the same base, add exponents: $$a^m \cdot a^n = a^{m+n}$$. - When dividing powers with the same base, subtract exponents: $$\frac{a^m}{a^n} = a^{m-n}$$. - Any number to the zero power is 1: $$a^0 = 1$$. 3. **Simplify the first big parenthesis:** $$5^8 \cdot 5^4 \cdot 5 = 5^{8+4+1} = 5^{13}$$ Now divide by $$5^{11}$$: $$\frac{5^{13}}{5^{11}} = 5^{13-11} = 5^2$$ 4. **Simplify the second big parenthesis numerator:** $$15^6 \cdot 15 = 15^{6+1} = 15^7$$ Divide by $$15^3$$: $$\frac{15^7}{15^3} = 15^{7-3} = 15^4$$ 5. **Simplify the denominator:** $$\left(\frac{30}{2}\right)^3 = 15^3$$ 6. **Put it all together:** $$\left(5^2\right) \cdot 3^0 - \frac{15^4}{15^3}$$ Since $$3^0 = 1$$: $$5^2 \cdot 1 - 15^{4-3} = 25 - 15^1 = 25 - 15$$ 7. **Final calculation:** $$25 - 15 = 10$$ **Answer:** $$10$$