Full solution

\frac{\text { № } 1}{\text { Сравнить } 80^{13} \times 10^{28}}

Express as Product: Now, let's express $80^{13}$ as $(2^4 \times 5)^{13}$ .
Apply Power Rule: Using the power of a product rule, $(a*b)^n = a^n * b^n$ , we get $2^{4*13} * 5^{13}$ .
Calculate Exponents: So, $2^{4\times13}$ is $2^{52}$ and $5^{13}$ remains the same. Now we have $2^{52} \times 5^{13}.$
Multiply by $10^{28}$ : Next, let's multiply $2^{52} \times 5^{13}$ by $10^{28}$ . Since $10$ is $2\times5$ , we can write $10^{28}$ as $2^{28} \times 5^{28}$ .
Combine Exponents: Now we multiply the exponents with the same base: $2^{52} \times 2^{28}$ and $5^{13} \times 5^{28}.$
Final Answer: Adding the exponents for the same bases gives us $2^{(52+28)}$ and $5^{(13+28)}$ .
Final Answer: Adding the exponents for the same bases gives us $2^{52+28}$ and $5^{13+28}$ .So, $2^{52+28}$ is $2^{80}$ and $5^{13+28}$ is $5^{41}$ . Now we have $2^{80} \times 5^{41}$ .
Final Answer: Adding the exponents for the same bases gives us $2^{52+28}$ and $5^{13+28}$ .So, $2^{52+28}$ is $2^{80}$ and $5^{13+28}$ is $5^{41}$ . Now we have $2^{80} \times 5^{41}$ .Finally, we combine the exponents with the same base to get the final answer: $2^{80} \times 5^{41}$ .