Answer:
2nd file is [tex]3^5=243[/tex] kilobytes greater than 1st file.
Step-by-step explanation:
We have been given that a file on the hard drive of the computer is [tex]3^2[/tex] kilobytes another file is [tex]3^7[/tex] kilobytes. We are asked to find how many times larger is the second filed in the first file.
To solve our given problem, we will divide kilobytes in 2nd file by kilobytes in 1st file.
[tex]\text{Number of times 2nd file is greater than 1st file}=\frac{3^7}{3^2}[/tex]
Using exponent quotient property [tex]\frac{a^m}{a^n}=a^{m-n}[/tex], we will get:
[tex]\text{Number of times 2nd file is greater than 1st file}=3^{7-2}[/tex]
[tex]\text{Number of times 2nd file is greater than 1st file}=3^{5}[/tex]
Therefore, 2nd file is [tex]3^5[/tex] kilobytes greater than 1st file.
