Simplifying $(m^3)^4(2x^3)^7(m^2)^5(3x)^2$

Question

I am having trouble with simplifying the following algebraic expression:

$$(m^3)^4(2x^3)^7(m^2)^5(3x)^2$$

I have been able to do the exponents and all the other equations I needed to simplify but not this one. If somebody could provide a step by step solution to the equation then that would be greatly appreciated.

Answer 1

Ok, so you want to simplify $$ (m^3)^4(2x^3)^7(m^2)^5(3x)^2 $$ As the other answer attempts to, you can focus on each factor on its own. You simply use the rules that

• $x^ax^b = x^{a+b}$ and
• $(x^a)^b = x^{ab}$ and
• $(xy)^{a} = x^ay^a$

So $$ \begin{align} (m^3)^4 &= m^{3\cdot 4} = m^{12} \\ (2x^3)^7 &= 2^7(x^3)^7 = 2^7x^{21}\\ (m^2)^5 &= m^{10}\\ (3x)^2 &= 3^2x^2 \end{align} $$ So $$\begin{align} (m^3)^4(2x^3)^7(m^2)^5(3x)^2 &= m^{12}2^7x^{21}m^{10}3^2x^2 \\ &= 2^73^2m^{12}m^{10}x^{21}x^{2} \\ &= 2^73^2m^{22}x^{23} \end{align} $$