What percentage of the atoms in the same sample of plutonium-238 will have changed to another isotope after 263.1 years?

(263.1 years) x (half-life / 87.7 years)  =  3 half-lifes In 3 half-lifes, (1/2 x 1/2 x 1/2) = 1/8 of the atoms in a sample remain unchanged. That's 12.5% that remain unchanged. The other 87.5% of the atoms in the sample have decayed, and changed to either other isotopes of plutonium or into atoms of other elements.

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: