Question

product of (3/2 p²q²) × (-2/3 p²q³) × (2 p²q²)​

Answer 1

♣ Qᴜᴇꜱᴛɪᴏɴ :

$\sf{\mathrm{Simplify}\:\left(\dfrac{3}{2}p^2q^2\right)\times \left(-\dfrac{2}{3}p^2q^3\right)\times \left(2p^2q^2\right)}$

★═══════════════════════★

 

♣ ᴀɴꜱᴡᴇʀ :

$\sf{\left(\dfrac{3}{2}p^2q^2\right)\times \left(-\dfrac{2}{3}p^2q^3\right)\times \left(2p^2q^2\right)=\quad -2p^6q^7}$

★═══════════════════════★

♣ ᴄᴀʟᴄᴜʟᴀᴛɪᴏɴꜱ :

$\mathrm{Apply\:the\:rule}:\quad \:a\left(-b\right)=-ab$

$\left(\dfrac{3}{2}p^2q^2\right)\left(-\dfrac{2}{3}p^2q^3\right)=-\dfrac{3}{2}p^2q^2\dfrac{2}{3}p^2q^3$

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

$p^2p^2p^2=p^{2+2+2}$

$=-\dfrac{3}{2}p^{2+2+2}q^2\dfrac{2}{3}q^3\times \:2q^2$

$=-\dfrac{3}{2}p^6q^2\dfrac{2}{3}q^3\times \:2q^2$

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

$q^2q^3q^2=q^{2+3+2}$

$=-\dfrac{3}{2}p^6q^{2+3+2}\dfrac{2}{3}\times \:2$

$=-\dfrac{3}{2}p^6q^7\dfrac{2}{3}\times \:2$

$\large\boxed{\sf{=-2p^6q^7}}$