Question

Solve THis Using Exponent laws

(8^2)^6 PLEASE HELP ME I REALLY NEEDE HELP FAST

Answer 1

\[\Huge 8^{2 \times 6}\]

Answer 2

but doesnt the 8 also get timesde by the six

Answer 3

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

Answer 4

so 8x6 = 48^12

Answer 5

what? Where did that come from?

Answer 6

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

Answer 7

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?

Answer 8

ohhhhhhhhhhhh

Answer 9

In the same way, \( (8^2)^6 \) means \(8^2 \) multiplied by itself 6 times:
\[ (8^2)^6 = (8^2) \times (8^2) \times (8^2) \times (8^2) \times (8^2) \times (8^2) \]

Answer 10

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.