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waheguru

  • 4 years ago

Solve THis Using Exponent laws (8^2)^6 PLEASE HELP ME I REALLY NEEDE HELP FAST

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  1. saifoo.khan
    • 4 years ago
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    \[\Huge 8^{2 \times 6}\]

  2. waheguru
    • 4 years ago
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    but doesnt the 8 also get timesde by the six

  3. JamesJ
    • 4 years ago
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    \[ (8^2)^6 = 8^2 . 8^2 . 8^2 . 8^2 . 8^2 . 8^2 \ \text{ (six times) } \] \[ = 8^{2+2+2+2+2+2} \] \[ = 8^{2 \times 6} \] \[ = 8^{12} \]

  4. waheguru
    • 4 years ago
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    so 8x6 = 48^12

  5. JamesJ
    • 4 years ago
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    what? Where did that come from?

  6. waheguru
    • 4 years ago
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    doesnt the 8 also get multiplyed by 8 or does it stay the same

  7. JamesJ
    • 4 years ago
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    By definition \( 8^{12} \) means 8 multiplied by itself 12 times \[ 8^{12} = 8 \times 8 \times 8 \times 8 \times 8 \times 8 \times 8 \times 8 \times 8 \times 8 \times 8 \times 8 \] Does that answer your question?

  8. waheguru
    • 4 years ago
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    ohhhhhhhhhhhh

  9. JamesJ
    • 4 years ago
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    In the same way, \( (8^2)^6 \) means \(8^2 \) multiplied by itself 6 times: \[ (8^2)^6 = (8^2) \times (8^2) \times (8^2) \times (8^2) \times (8^2) \times (8^2) \]

  10. JamesJ
    • 4 years ago
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    That is why the general law is \[ (x^a)^b = x^{ab} \] For your problem then, you can see that we use that law to immediately conclude that \[ (8^2)^6 = 8^{12} \] But you also see from above why that law makes sense and why in this particular case, the result is indeed true.

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