Question

using exponents, what is the simplified form of the expression (-4m³n⁴)³

Explanation:

Step1: Apply power - of - a - product rule

$(-4m^{3}n^{4})^{3}=(-4)^{3}\times(m^{3})^{3}\times(n^{4})^{3}$

Step2: Calculate $(-4)^{3}$

$(-4)^{3}=(-4)\times(-4)\times(-4)= - 64$

Step3: Apply power - of - a - power rule for $m$ and $n$

$(m^{3})^{3}=m^{3\times3}=m^{9}$ and $(n^{4})^{3}=n^{4\times3}=n^{12}$

Step4: Combine results

$(-4)^{3}\times(m^{3})^{3}\times(n^{4})^{3}=-64m^{9}n^{12}$

Answer:

$-64m^{9}n^{12}$