Question

Simplifying Rational Expressions

Answer 1

That would be 7 because 

b^4 / b^-3  = b^(4-(-3)) = b^7

Answer 2

The given expression to simplify is

$\frac{-4a^{-2}b^4}{8a^{-6}b^{-3}} , \text{Assuming that } a\neq 0, b\neq 0.$

We can Simplify the given rational expression using the following exponent property

$\frac{1}{a^m}=a^{-m}, \frac{1}{a^{-m}}=a^m\\ \\ a^m*a^n=a^{m+n}\\ \\ \text{Now re-write the given expression as below}$

$\frac{-4a^{-2}b^4}{8a^{-6}b^{-3}} =\frac{-4}{8} *\frac{a^{-2}}{a^{-6}} *\frac{b^4}{b^{-3}} \\ \\ \text{Now apply the exponent property and simplify}\\ \\ =\frac{-1}{2} *a^{-2}*a^6*b^4*b^3\\ \\ \text{Again apply the exponent property and simplify we get}\\ \\ =\frac{-1}{2} *a^{-2+6}*b^{4+3}\\ \\ =\frac{-1}{2} a^4b^7$

Hence exponent of the variable b is 7