Question

(x^6)(x^2)

Answer 1

how would i go about this ? @mathstudent55

Answer 2

well, when multiplying with the same base.... you would add the exponents

Answer 3

so it would be x^6+2

Answer 4

x^(6+2)

Answer 5

then simplify

Answer 6

so x^8 ?

Answer 7

yup

Answer 8

Same base, add exponents.

Answer 9

thanks @trindawg @AlexandervonHumboldt2

Answer 10

Correct.

Answer 11

This is why you add the exponents when you multiply two powers with the same base.
I'll use your problem as an example.

power 6 means 6 x's power 2 means 2 x's
\((x^6)(x^2) = ~~~~~~~~~~~~xxxxxx ~~~~~~~~~~~~~~~~~~~\times~~~~~~~~~~~~~~~~~ xx\)

now we have 8 x's
\((x^6)(x^2) =~~~~~~~ xxxxxxxx\)

8 x's mean an exponent of 8
\((x^6)(x^2) = ~~~~~~~~~x^8\)

8 = 6 + 2

\((x^6)(x^2) = x^{6 + 2} = x^8\)

In general:
\(a^m \times a^n = a^{m + n} \)