Questions: 7^6 ÷ 7^2 = 1^8 7^3 7^4

Solution Steps

To solve the expression $7^{6} \div 7^{2}$, we can use the properties of exponents. Specifically, when dividing like bases, we subtract the exponents. Therefore, the expression simplifies to $7^{(6-2)} = 7^{4}$.

To simplify the expression $7^{6} \div 7^{2}$, we apply the rule for dividing powers with the same base: subtract the exponents. Thus, the expression becomes: $$7^{6} \div 7^{2} = 7^{(6-2)} = 7^{4}$$

Next, we calculate the value of $7^{4}$: $$7^{4} = 7 \times 7 \times 7 \times 7 = 2401$$

The options provided are:

• $1^{8} = 1$
• $7^{3} = 343$
• $7^{4} = 2401$

The calculated value $2401$ matches the option $7^{4}$.

Final Answer