Any non-zero variable or number raised to the zero power simplifies to exactly 1. Thus, as long as x is not zero, x^0 = 1.

According to the zero exponent rule, any non-zero real number raised to the power of zero is always equal to 1. Therefore, 5^0 equals 1.

Using the power rule, multiply the inner exponent 2 by the outer exponent 2. This gives an exponent of 4, keeping the base 7 intact to form 7^4.

When a term with an exponent is raised to an additional power, the exponents are multiplied. Multiplying 3 by 5 yields 15, making the simplified term z^15.

Multiplying the exponent 5 by the outer exponent 3 gives 15. The base remains 4, so the final simplified answer is 4^15.

By multiplying the exponents according to the power of a power rule, we calculate 4 * 2 = 8. The base stays the same, resulting in 10^8.

The rule for a power raised to a power requires multiplying the exponents. Calculating 2 times 6 gives 12, so the expression becomes a^12.

When an exponential term is raised to a power, multiply the exponents. Here, multiplying 3 by 3 gives an exponent of 9, leaving us with 5^9.

Applying the power rule, we multiply the exponent inside the parentheses by the exponent outside. The product of 5 and 2 is 10, so the expression simplifies to y^10.

To simplify a base raised to a power and then raised to another power, multiply the two exponents together. Multiplying 2 and 4 gives 8, resulting in 3^8.