Expponents and Powers

What is the value of \( 5^0 \)?

Simplify \( (2^3)^4 \).

If \( a^m \times a^n = a^{12} \) and \( m - n = 4 \), find the values of \( m \) and \( n \) given both are positive integers.

Express \( \frac{3^5}{3^2} \) as a single power of 3.

Simplify \( (16)^{3/4} \).

If \( x^3 = 27 \), find the value of \( x^{-2} \).

Which of the following is equal to \( \frac{1}{a^{-3}} \) where \( a \neq 0 \)?

Simplify \( (x^2 y^{-3})^{-2} \).

Evaluate \( \left(\frac{2}{3}\right)^{-3} \).

If \( 9^{x} = 27 \), find the value of \( x \).