What does (x^a)^b equal according to exponent rules?

The expression ( (x^a)^b ) can be simplified using the power of a power rule in exponents. This rule states that when raising a power to another power, you multiply the exponents. Therefore, ( (x^a)^b ) simplifies to ( x^{a \cdot b} ).

This means that the base ( x ) retains its value while the exponents ( a ) and ( b ) are combined through multiplication. Consequently, ( (x^a)^b ) is equal to ( x^{ab} ), which confirms that the correct answer is indeed ( x^{ab} ).

Understanding this rule is fundamental as it applies universally to any base and any exponents, allowing for consistent simplification across various algebraic contexts.