Questions: 7^6 ÷ 7^2 = 1^8 7^3 7^4

Transcript text: $7^{6} \div 7^{2}=$ $1^{8}$ $7^{3}$ $7^{4}$

Solution

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 $7^{(6-2)} = 7^{4}$.

Step 1: Simplify the Expression Using Exponent Rules

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: \[ 7^{6} \div 7^{2} = 7^{(6-2)} = 7^{4} \]

Step 2: Calculate the Value of $7^{4}$

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

Step 3: Compare with Given Options

The options provided are: