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calculusxy

  • one year ago

Help with exponents! (x^4)^{-3} x 2x^4

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  1. rishavraj
    • one year ago
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    \[(a^x)^y = a^{xy}~~~~~~~~~a^x \times a^y = a^{x + y}\]

  2. calculusxy
    • one year ago
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    Sorry i meant 1/x^12 x 2x^4

  3. rishavraj
    • one year ago
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    hmmm v???

  4. calculusxy
    • one year ago
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    No i wrote x

  5. rishavraj
    • one year ago
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    okay see(x^4)^{-3} = x^{-12}

  6. calculusxy
    • one year ago
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    Yes...

  7. rishavraj
    • one year ago
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    now u got \[x^{-12} \times 2 \times x^4\] so use a^x + a^y = a^{x + y}

  8. calculusxy
    • one year ago
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    x^{-8}

  9. rishavraj
    • one year ago
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    question is \[(x^4)^{-3} \times 2x^4\]

  10. calculusxy
    • one year ago
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    Yes

  11. rishavraj
    • one year ago
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    so u got 2*x*{-8} u can write it as 2/(x^{}8) or just 2x^{-8}

  12. calculusxy
    • one year ago
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    I dont understand

  13. rishavraj
    • one year ago
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    u know \[\frac{ 1 }{ a^x } = a^{-x}\]

  14. rishavraj
    • one year ago
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    so here u having \[2x^{-8}\] just leave it tht way :)

  15. calculusxy
    • one year ago
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    But why do i need to combine them? R they like terms and, if so, why?

  16. Nnesha
    • one year ago
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    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
    • one year ago
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    \(\color{blue}{\text{Originally Posted by}}\) @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
    • one year ago
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    that's for negative exponent rule he gave u^^^^

  19. Nnesha
    • one year ago
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    \(\color{blue}{\text{Originally Posted by}}\) @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
    • one year ago
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    So the 2 doesn't matter? @Nnesha

  21. Nnesha
    • one year ago
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    multiply the coefficient x is same as 1x \[\huge\rm1 x^{-12} \times 2x^4=(1 \times 2)x^{-12+4}\]

  22. calculusxy
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    coefficient *

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