## waheguru 4 years ago Solve THis Using Exponent laws (8^2)^6 PLEASE HELP ME I REALLY NEEDE HELP FAST

1. saifoo.khan

$\Huge 8^{2 \times 6}$

2. waheguru

but doesnt the 8 also get timesde by the six

3. JamesJ

$(8^2)^6 = 8^2 . 8^2 . 8^2 . 8^2 . 8^2 . 8^2 \ \text{ (six times) }$ $= 8^{2+2+2+2+2+2}$ $= 8^{2 \times 6}$ $= 8^{12}$

4. waheguru

so 8x6 = 48^12

5. JamesJ

what? Where did that come from?

6. waheguru

doesnt the 8 also get multiplyed by 8 or does it stay the same

7. JamesJ

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

ohhhhhhhhhhhh

9. JamesJ

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

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.