## calculusxy one year ago Help with exponents! (x^4)^{-3} x 2x^4

1. rishavraj

$(a^x)^y = a^{xy}~~~~~~~~~a^x \times a^y = a^{x + y}$

2. calculusxy

Sorry i meant 1/x^12 x 2x^4

3. rishavraj

hmmm v???

4. calculusxy

No i wrote x

5. rishavraj

okay see(x^4)^{-3} = x^{-12}

6. calculusxy

Yes...

7. rishavraj

now u got $x^{-12} \times 2 \times x^4$ so use a^x + a^y = a^{x + y}

8. calculusxy

x^{-8}

9. rishavraj

question is $(x^4)^{-3} \times 2x^4$

10. calculusxy

Yes

11. rishavraj

so u got 2*x*{-8} u can write it as 2/(x^{}8) or just 2x^{-8}

12. calculusxy

I dont understand

13. rishavraj

u know $\frac{ 1 }{ a^x } = a^{-x}$

14. rishavraj

so here u having $2x^{-8}$ just leave it tht way :)

15. calculusxy

But why do i need to combine them? R they like terms and, if so, why?

16. Nnesha

these are the exponents rules when we multiply same bases we should add exponents $\huge\rm x^m \times x^n=x^{m+n}$ and when we divide same base , subtract their exponents $\huge\rm \frac{ x^m }{ x^n }=x^{m-n}$

17. Nnesha

$$\color{blue}{\text{Originally Posted by}}$$ @rishavraj u know $\frac{ 1 }{ a^x } = a^{-x}$ $$\color{blue}{\text{End of Quote}}$$ if there is negative exponents we should flip the fraction when we flip the fraction sign of the exponent would change

18. Nnesha

that's for negative exponent rule he gave u^^^^

19. Nnesha

$$\color{blue}{\text{Originally Posted by}}$$ @calculusxy But why do i need to combine them? R they like terms and, if so, why? $$\color{blue}{\text{End of Quote}}$$ like base

20. calculusxy

So the 2 doesn't matter? @Nnesha

21. Nnesha

multiply the coefficient x is same as 1x $\huge\rm1 x^{-12} \times 2x^4=(1 \times 2)x^{-12+4}$

22. calculusxy

Okay so 2x^4 has two terms right? Since 2 is being multiplied with x^4, the two is one term and x^4 is another?

23. Nnesha

sorry for late reply not getting notification so plz tag the username :=) no 2x^4 is only one term not two terms: number or variable that are separated by + or - sign

24. Nnesha

so 2x^4 is only one term when we multiply we should focus on the base when you ADD or subtract  like terms u just have to deal with the coefficients like $2x+3x=(2+3)x$ but when we multiply same bases we should add their exponents and multiply the coefficien$\huge\rm \color{Red}{1}x^m · \color{blue}{1}x^n=(\color{red}{1} ·\color{blue}{1})x^{m+n}$ts as well

25. Nnesha

coefficient *