Question

1. the expression ((x^{-3}x^{7})^{-2}) is equivalent to (x^{m}). what is the value of (m)? enter your answer in the space provided.

Explanation:

Step1: Simplify inside the parentheses

When multiplying exponents with the same base, we add the exponents. So \( x^{-3} \cdot x^{7} = x^{-3 + 7} = x^{4} \).

Step2: Apply the outer exponent

Now we have \( (x^{4})^{-2} \). When raising a power to a power, we multiply the exponents. So \( x^{4 \cdot (-2)} = x^{-8} \).
Since the expression is equivalent to \( x^{m} \), then \( m = -8 \).

Answer:

-8