Subtract the exponents: 3 - 5 = -2, giving 8^-2. A negative exponent indicates a reciprocal, so 8^-2 = 1 / (8^2) = 1/64.

Subtracting the exponents yields 7^(2-2) = 7^0. Any non-zero base raised to the power of 0 is equal to 1. Alternatively, dividing a number by itself equals 1.

Subtract the exponents: 4 - (-1) = 4 + 1 = 5. The expression becomes 3^5. Evaluating 3^5 gives 3 * 3 * 3 * 3 * 3 = 243.

When dividing terms with the same base, subtract the bottom exponent from the top exponent. x^(8-3) simplifies to x^5.

Applying the quotient law, 10^5 / 10^2 = 10^(5-2) = 10^3. 10^3 equals 10 * 10 * 10, which is 1,000.

Using the division rule for indices, subtract the powers: 6 - 4 = 2. This leaves 5^2. Evaluating 5^2 gives 25.

According to the quotient law of indices, when dividing expressions with the same base, you subtract the exponent of the denominator from the exponent of the numerator. So, 2^(5-2) = 2^3.

Add the exponents: -1 + 3 = 2. The expression simplifies to 6^2. Calculating the square of 6 yields 6 * 6 = 36.

Using the indices addition rule for the same base (-2), we get (-2)^(2+3) = (-2)^5. A negative number raised to an odd power remains negative, so (-2)^5 = -32.

By adding the exponents, 7^1 * 7^2 = 7^(1+2) = 7^3. Calculating 7^3 gives 7 * 7 * 7 = 343.