Find the missing exponent. Set up an equation and solve. : (3a^3)^n · 2a^3 = 18a^9

N = missing exponent.

Please explain so I can understand.

Question

Find the missing exponent. Set up an equation and solve. : (3a^3)^n · 2a^3 = 18a^9

N = missing exponent.

Please explain so I can understand.

kinggeorge · Answer

The original statement is$$[3(a^n)]^n \cdot 2(a^3)=18(a^9)$$correct?

kinggeorge · Answer

with a 3 instead of an n for that very first $a^n$

anonymous · Answer

No, I meant: $$(3a ^{3})^{n} · 2a ^{3} = 18a ^{9}$$

kinggeorge · Answer

Then$$(3a^3)^n = (3^n)((a^3)^n)= 3^n \cdot a^{3n}$$If we multiply that by $2(a^3)$, we get$$ 3^n \cdot a^{3n}\ \cdot 2(a^3)=2\cdot 3^n \cdot a^{3n+3}$$Finally, we set this equal to $18a^9$ so that $$2\cdot 3^n \cdot a^{3n+3}=18a^9$$Here, notice that $3n+3=9$since the exponents on $a$ must be the same. Solving for $n$, we get that $n=2$.If we check our answer, $$2\cdot 3^2 \cdot a^{3\cdot2+3}=2\cdot9\cdot a^9=18a^9$$Since this works, we are done, and $n=2$.

anonymous · Answer

THANK YOU SO MUCH

kinggeorge · Answer

You're welcome.