Apply the properties of exponents including: multiplying, dividing, power to a power, zero exponent, negative exponents, and turning fractional exponents into radicals. (copy)

Product Rule

When multiplying powers with the same base, add the exponents: $x^a imes x^b = x^{a+b}$.

Quotient Rule

When dividing powers with the same base, subtract the exponent in the denominator from the exponent in the numerator: $\frac{x^a}{x^b} = x^{a-b}$.

Power to a Power Rule

When a power is raised to another power, multiply the exponents: $(x^a)^b = x^{ab}$.

Zero Exponent Rule

Any non-zero base raised to the power of zero is always $1$.

Negative Exponent Rule

A negative exponent signifies a reciprocal relationship: $x^{-n} = \frac{1}{x^n}$.

Fractional Exponents

A rational exponent can be expressed in radical form: $x^{m/n} = \text{n-th root of } x^m$.