Question

3^2x × 3^2x/3^2= 4√3^20 (genius, here u go)​

Answer 1

Answer:

$\dfrac{3^{2x}\times \:3^{2x}}{3^2}=\sqrt[4]{3^{20}}\quad :\quad x=\dfrac{7}{4}\quad \left(\mathrm{Decimal}:\quad x=1.75\right)$

Step-by-step explanation:

$\dfrac{3^{2x}\times \:3^{2x}}{3^2}=\sqrt[4]{3^{20}}$

$\mathrm{Apply\:exponent\:rule}:\quad \dfrac{1}{a^b}=a^{-b}$

$\dfrac{1}{3^2}=3^{-2}$

$3^{2x}\times \:3^{2x}\times \:3^{-2}=\sqrt[4]{3^{20}}$

$\mathrm{Apply\:exponent\:rule}:\quad \:a^b\times \:a^c=a^{b+c}$

$3^{2x}\times \:3^{2x}=3^{2x+2x}$

$3^{2x+2x}\times \:3^{-2}=\sqrt[4]{3^{20}}$

$\mathrm{Divide\:both\:sides\:by\:}3^{-2}$

$\dfrac{3^{2x+2x}\times \:3^{-2}}{3^{-2}}=\dfrac{\sqrt[4]{3^{20}}}{3^{-2}}$

Simplify;

$3^{2x+2x}=\dfrac{\sqrt[4]{3^{20}}}{3^{-2}}$

$\mathrm{Simplify\:}\dfrac{\sqrt[4]{3^{20}}}{3^{-2}}:\quad 2187$

$3^{2x+2x}=2187$

$\mathrm{Convert\:}2187\mathrm{\:to\:base\:}3$

$2187=3^7$

$3^{2x+2x}=3^7$

$\mathrm{If\:}a^{f\left(x\right)}=a^{g\left(x\right)}\mathrm{,\:then\:}f\left(x\right)=g\left(x\right)$

$2x+2x=7$

Simplify;

$4x=7$

$\mathrm{Solve\:}\:4x=7:\quad x=\dfrac{7}{4}$

$\bold{x=\dfrac{7}{4}}$