The power of a power rule dictates that we multiply the inner and outer exponents. Therefore, 4 multiplied by 3 gives 12, making the simplified form x^12.

When raising a power to another power, you multiply the exponents. Multiplying the inside exponent 3 by the outside exponent 2 yields an exponent of 6, resulting in 2^6.

Subtracting the exponents gives 8^(4-4) = 8^0. Any non-zero base raised to the power of zero equals 1. Alternatively, any number divided by itself is 1.

By applying the quotient rule for exponents, we subtract the bottom exponent (5) from the top exponent (12). This operation yields z^7.

Since the bases are the same, we simply subtract the exponents. Subtracting 3 from 9 leaves an exponent of 6, making the simplified form 4^6.

The quotient rule dictates subtracting the denominator's exponent from the numerator's. Performing 5 - 2 yields 3, giving a final simplified expression of 10^3.

Subtracting the exponents 8 - 7 gives 1. Any variable raised to the power of 1 is just the variable itself, so a^1 is written simply as a.

Applying the exponent rule for division, subtract the exponent 4 from the exponent 6 while maintaining the base of 5. This results in 5^2.

For division of terms with identical bases, subtract the lower power from the upper power. Taking 3 away from 10 gives an exponent of 7, making the answer y^7.

Using the quotient rule, we keep the base of 3 and subtract the denominator's exponent from the numerator's exponent. The calculation 7 - 2 leaves us with 3^5.