Question

Simplify the expression using properties of exponents. 25a^-5b^-8/5a^4b

Answer 1

Answer: The simplification is $5*a^{-9}*b^{-9}$

Step-by-step explanation:

Here we need to use the property:

$\frac{a^n}{a^m} = a^{n - m}$

We have the expression:

$\frac{25*a^{-5}*b^{-8}}{5*a^{4}*b}$

We can separate it in parts with the same base, then we can rewrite this as:

$\frac{25*a^{-5}*b^{-8}}{5*a^{4}*b} = \frac{25}{5} \frac{a^{-5}}{a^4} \frac{b^{-8}}{b}$

Using the first property we can rewrite this as:

$\frac{25}{5} \frac{a^{-5}}{a^4} \frac{b^{-8}}{b} = 5*a^{-5 - 4}*b^{-8 - 1} = 5*a^{-9}*b^{-9}$