Question

Simplify and express the answer in the positive exponent form:​
(v) $\frac{a^{-7}\times b^{-7}\times c^5\times d^4}{a^3\times b^{-5}\times c^{-3}\times d^8}$

Answer 1

Given: $\frac{a^{-7}\times b^{-7}\times c^5\times d^4}{a^3\times b^{-5}\times c^{-3}\times d^8}$

It can be written as:
$\frac{a^{-7}\times b^{-7}\times c^5\times d^4}{a^3\times b^{-5}\times c^{-3}\times d^8}=a^{-7-3}\times b^{-7-(-5)}\times c^{5-(-3)}\times d^{4-8}$

[$\because$$\frac{a^m}{a^n}=a^{m-n}$]
On further calculation, we have :
$a^{-10}\times b^{-2}\times c^8\times d^{-4}=\frac{c^8}{a^{10}\times b^2\times d^4}$

Hence, $\frac{a^{-7}\times b^{-7}\times c^5\times d^4}{a^3\times b^{-5}\times c^{-3}\times d^8}=\frac{c^8}{a^{10}\times b^2\times d^4}$.