kaylala 2 years ago (3^2n times a^3)^2 = ?

1. TjRoDz

hmm does it have choices? my answer is 9a^6n but i could be wrong

2. kaylala

$(3^{4n}a ^{3})^{2^{}} = ???$

3. TjRoDz

ok sorry i was wrong

4. kaylala

@TjRoDz you're wrong...

5. TjRoDz

uhh 81a^6n

6. kaylala

still wrong @TjRoDz

7. TjRoDz

hhhaha my pea sized brain

8. kaylala

9. thomaster

uhm i think $$\sf\Large a^6\large3^{\Large8n}$$

10. thomaster

$$\Large (a^n)^m=a^{n*m}$$

11. kaylala

wont it be instead of 3 it would be squared and be 9?

12. kaylala

@thomaster wont it be: instead of 3; it would be squared and be 9?

13. kaylala

i'm confused

14. thomaster

No $$\Large(3^{4n}a ^3)^2$$ 4*2=8 and 3*2=6 $$\Large3^{8n}a ^6~\to~a^63^{8n}$$

15. phi

you can memorize the rule $(x^a)^b = x^{ab}$ which means multiply the exponents but you can use this idea: $x^2 \text{ means } x \cdot x$ so $(3^{4n}a ^{3})^{2} \text{ means } (3^{4n}a ^{3})(3^{4n}a ^{3})$

16. phi

you can re-arrange that to $(3^{4n}\cdot 3^{4n}\cdot a ^{3}\cdot a ^{3})$

17. phi

if you don't know about "adding exponents" you could figure out $a^3 \cdot a^3$ by knowing that $$a^3 = a\cdot a \cdot a$$ $a^3 \cdot a^3 = a\cdot a \cdot a \cdot a\cdot a \cdot a= a^6$

18. phi

but to do $3^{4n} \cdot 3^{4n}$ you need to know the rule: if you have the same base, add the exponents $3^{4n+4n}$ or $3^{8n}$