Question

Write your answer as a power or as a product of powers. $$ -\left(r^{2} s t^{3}\right)^{2}\left(s^{4} t\right)^{3} $$

Short answer

The simplified form of the expression \(-\left(r^{2} s t^{3}\right)^{2}\left(s^{4} t\right)^{3}\) is \( - r^{4} * s^{14} * t^{9} \)

Step-by-step solution

Apply the power of a product property

The property of power of a product states that \( (ab)^n = a^n b^n \). So here we apply this principle to both terms: \[ - (r^{2} s t^{3})^{2}(s^{4} t)^{3} = - r^{2*2} * s^{2} * t^{3*2} * s^{4*3} * t^{3} \]

Simplify the expression

We then simplify the expression by performing the multiplication in each power: \[ - r^{2*2} * s^{2} * t^{3*2} * s^{4*3} * t^{3} = - r^{4} * s^{2} * t^{6} * s^{12} * t^{3} \]

Combine like terms

Now we combine the like terms. The terms \(s^2\) and \(s^{12}\) become \(s^{2+12}\), and similarly, \(t^6\) and \(t^3\) become \(t^{6+3}\): \[ - r^{4} * s^{2} * t^{6} * s^{12} * t^{3} = - r^{4} * s^{14} * t^{9} \]