Question

simplify. express your answer using exponents.
$(r^{-2}s^{3}t^{-4})^{7}$

Explanation:

Step1: Apply power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). So, for \((r^{-2}s^{3}t^{-4})^{7}\), we can apply this rule to each factor: \(r^{-2\times7}s^{3\times7}t^{-4\times7}\).

Step2: Calculate the exponents

Calculate each exponent: \(-2\times7 = -14\), \(3\times7 = 21\), and \(-4\times7 = -28\). So the expression becomes \(r^{-14}s^{21}t^{-28}\).

Answer:

\(r^{-14}s^{21}t^{-28}\)