Multiply and simplify. Assume that variables represent nonzero real numbers.

Question

a Superscript negative 4 Baseline times a Superscript 7 Baseline times a Superscript negative 9
 

Answer 1

To multiply the expressions \( a^{-4} \cdot a^{7} \cdot a^{-9} \), we can use the property of exponents that states \( a^m \cdot a^n = a^{m+n} \).

Now, perform the addition of the exponents:

\[ -4 + 7 + (-9) \]

Calculating this step-by-step:

1. \(-4 + 7 = 3\)
2. \(3 - 9 = -6\)

Thus, we combine the exponents:

\[ a^{-4} \cdot a^{7} \cdot a^{-9} = a^{-6} \]

Since \( a^{-6} \) can be simplified further using the negative exponent rule \( a^{-n} = \frac{1}{a^n} \):

\[ a^{-6} = \frac{1}{a^6} \]

So the final simplified result is:

\[ \frac{1}{a^6} \]