Final answer:
To simplify (2.6 x 10^5)^2, first square the coefficient (2.6^2 = 6.76) and then the power of ten (10^5 squared becomes 10^10), resulting in 6.76 x 10^10 which is converted to scientific notation by adjusting the coefficient to be 6.7 with an exponent of 11 (6.7 x 10^11).
Step-by-step explanation:
To simplify the expression (2.6 x 10^5)^2 and write the answer in scientific notation, you should square both the coefficient (2.6) and the power of ten (10^5).
First, square the coefficient:
2.6^2 = 6.76
Then, apply the rule for exponents when squaring a power of ten:
(10^5)^2 = 10^(5*2) = 10^10
Combine the squared coefficient with the new power of ten:
6.76 x 10^10
However, in scientific notation, the coefficient must be between 1 and 10. Thus, we shift the decimal point one place to the left:
6.76 becomes 6.76 -> 6.7 (rounded to one decimal place)
Since we moved the decimal one place to the left, we must increase the exponent by 1 to maintain the equivalence:
6.7 x 10^(10+1)
Therefore, the final answer in scientific notation is:
6.7 x 10^11