Question

simplify. express your answer using positive exponents.
$a^{-1}b^{6}c^{72} \cdot a^{0}b^{4}c^{-1} \cdot a^{-98}b^{2}c^{0}$

Explanation:

Step1: Combine like bases for \(a\)

When multiplying terms with the same base, we add the exponents. For \(a\): \(-1 + 0 + (-98)=-99\).

Step2: Combine like bases for \(b\)

For \(b\): \(6 + 4 + 2 = 12\).

Step3: Combine like bases for \(c\)

For \(c\): \(72+(-1)+0 = 71\).

Step4: Convert negative exponents to positive

We know that \(a^{-n}=\frac{1}{a^{n}}\), so \(a^{-99}=\frac{1}{a^{99}}\). Combining with the other terms, we have \(\frac{b^{12}c^{71}}{a^{99}}\).

Answer:

\(\frac{b^{12}c^{71}}{a^{99}}\)