Question

3^8 x 3^4/3^8 x 3^2

Answer 1

(9)

=3^8×3^4/3^8×2^2

=6561×81/6561×9

=81/9

=9

Answer 2

`3^(6)` or 729

Explanation:

`3^(8)`·
`(3^(4) )/(3^(8) )`·
`3^(2)` The Quotient of Powers Property tells us that if we are dividing with exponents that have the same base, we can subtract the exponents.

`3^(8)` ·
`3^(4-8)`·
`3^(2)`

`3^(8)` ·
`3^(-4)` ·
`3^(2)` The Product of Powers Property tells us that if the bases are the same when we are multiplying we can add the exponents.

`3^(6)`

Another way to look at it is to write it out in expanded form:

`(3x3x3x3x3x3x3x3x3x3x3x3x3x3)/(3x3x3x3x3x3x3x3)` When you cancel out the 3's that you have on the top and the bottom, you are left with 6 3's on the top.