Question

When simplified, the expression \[\left( w^{-5} \over w^{-9} \right)^{1\2} \] is equivalent to?

Answer 1

When you divide powers of the same base, you need to subtract the exponents. So, \[ \frac{w^{-5}}{w^{-9}}= w^{-5-(-9)} = w^4 \]The expression reduces to: \[ (w^4)^{1/2} \]When you raise a power to another exponent, you have to multiply the exponents. So: \[ (w^4)^{1/2}=w^{4(1/2)} = w^2 \]Which is the simplified expression.