(42y^-2x^4w^-6)/(7x^-3)y^(6w^-5)

To simplify the given expression, we can follow these steps:<br /><br />1. Divide the coefficients: $\frac{42}{7} = 6$<br />2. Apply the quotient rule for exponents: $x^{4-(-3)} = x^{4+3} = x^{7}$<br />3. Apply the quotient rule for exponents: $y^{-2-6} = y^{-8}$<br />4. Apply the quotient rule for exponents: $w^{-6-(-5)} = w^{-6+5} = w^{-1}$<br /><br />Putting it all together, we get:<br /><br />$\frac{42y^{-2}x^{4}w^{-6}}{7x^{-3}y^{6}w^{-5}} = 6x^{7}y^{-8}w^{-1}$<br /><br />Therefore, the simplified expression is $6x^{7}y^{-8}w^{-1}$.