Questions: Simplify the exponential expression. Assume that the variable represents a nonzero real number. (5 x^(-5))(9 x^(4)) (5 x^(-5))(9 x^(4))= (Type exponential notation with positive exponents.)

Solution Steps

To simplify the given exponential expression, we need to apply the properties of exponents. Specifically, we will multiply the coefficients and add the exponents of the same base.

1. Multiply the coefficients (5 and 9).
2. Add the exponents of \(x\) (-5 and 4).

We start with the expression \((5 x^{-5})(9 x^{4})\). The coefficients are 5 and 9. We multiply these coefficients: \[ 5 \times 9 = 45 \]

Next, we focus on the exponents of \(x\). The exponents are \(-5\) and \(4\). We add these exponents: \[ -5 + 4 = -1 \]

Combining the results from the previous steps, we have: \[ 45 x^{-1} \] To express this with positive exponents, we rewrite it as: \[ \frac{45}{x} \]

Final Answer