Question

Use the exponent properties to simplify the following 2x%29%5E4%7D" id="TexFormula1" title="\frac{(3x^2)^3}{(2x)^4}" alt="\frac{(3x^2)^3}{(2x)^4}" align="absmiddle" class="latex-formula">

Answer 1

Answer:

  $\dfrac{27}{16}x^2$

Step-by-step explanation:

The relevant properties are ...

  (a^b)^c = a^(bc)

  (a^b)/(a^c) = a^(b-c)

So, the expression simplifies to ...

  $\dfrac{(3x^2)^3}{(2x)^4}=\dfrac{3^3x^{2\cdot 3}}{2^4x^4}=\dfrac{27}{16}x^{6-4}=\dfrac{27}{16}x^{2}$