What does x to the power of a divided by x to the power of b equal?

When you divide exponential expressions with the same base, you subtract the exponents. This is derived from the properties of exponents, specifically the quotient rule, which states that for any nonzero number ( x ) and any real numbers ( a ) and ( b ):

[

\frac{x^a}{x^b} = x^{a-b}

]

In this case, applying the rule means that ( x ) raised to the power of ( a ) divided by ( x ) raised to the power of ( b ) simplifies to ( x^{a-b} ). Therefore, the expression correctly simplifies to ( x ) raised to the power of ( a ) minus ( b ), reflecting how the properties of exponents govern operations involving the same base.