How do you simplify this expression and eliminate all the negative exponents?

Question

((q⁻¹r⁻¹s⁻⁶) / (r⁻³sq⁻⁵))⁻¹

 

Simplify and eliminate all negative exponents.

 

 

Answer 1

Firstly, negative exponents means reciprocal. So to remove the negative exponent, from x^-1, you "flip it" to 1/x.

 

First part (q⁻¹r⁻¹s⁻⁶), would changed to ((1/q) * (1/r) * (1/s⁶)). Simplifying that gives (1 / (qrs⁶)).

Similarily with the second parth (r⁻³sq⁻⁵): ((1/r3) * s * (1/q⁵)). Simplifying: (s / q⁵r³)

 

So now we have ((1 / (qrs⁶)) / (s / q⁵r³))^-1. Before we deal with the last negative exponent, lets simplify the fractional division. Since we are dividing by a fraction, we simplify that to multplying by its reciprocal. Thus the (1 / (qrs⁶)) / (s / q⁵r³) can be rewrittten to: (1 / (qrs⁶)) * (q⁵r³ / s). Simplifying this further, we get: (q⁴r²) / s⁷.

 

Now to deal with the last negative exponent: ((q⁴r²) / s⁷)^-1

As before with negative exponents, we "flip", which result in: s⁷ / (q⁴r²)