Question

(\frac{a^{7}b^{8}c^{8}}{a^{5}bc^{7}})

Explanation:

Step1: Simplify the \(a\)-terms

When dividing exponents with the same base, we subtract the exponents. For the \(a\)-terms, we have \(a^{7}\div a^{5}\). Using the rule \( \frac{a^{m}}{a^{n}}=a^{m - n}\), we get \(a^{7-5}=a^{2}\).

Step2: Simplify the \(b\)-terms

For the \(b\)-terms, we have \(b^{8}\div b^{1}\) (since \(b = b^{1}\)). Using the same exponent rule, we get \(b^{8 - 1}=b^{7}\).

Step3: Simplify the \(c\)-terms

For the \(c\)-terms, we have \(c^{8}\div c^{7}\). Using the exponent rule, we get \(c^{8-7}=c^{1}=c\).

Step4: Combine the simplified terms

Now, we multiply the simplified \(a\), \(b\), and \(c\) terms together. So we have \(a^{2}\times b^{7}\times c=a^{2}b^{7}c\).

Answer:

\(a^{2}b^{7}c\)