Question

Can someone explain multiplying exponents to me please.

What is 2^2 x 2^2?
What is 2^2 x 7^4?

Please explain the laws and what not. Thank you!

Answer 1

For (a) we will add the exponents since the bases are same.

Answer 2

\[2^2\times7^4=(2\times2)\times(7\times7\times7\times7)\]

Answer 3

\[\Large a^b \times a^c = a^{b+c}\]

Answer 4

You can't really do much with exponents unless the bases are the same. Therefore, let's start by saying that you don't really do anything with the exponents unless they have the same base.
\[a^{2} * a^{5} = a^{2 + 5} = a^{7}\]
If the bases are the same and are being multiplied, you just add them.
\[(a^{2})^{3} = a^{2 * 3} = a^{6}\]
When a base and the exponent are being raised to a power with parentheses like shown, the exponents are multiplied.

Answer 5

Therefore, you can solve a, but for b, you can't really do much of anything except distribute the exponent and then multiply.

Answer 6

\[2^2\times7^4=(2\times2)\times(7\times7\times7\times7)\]\[\qquad\qquad=14^2\times7^2=98^2\]