The error in the work shown is in the third step because in third step same base property is not apply correctly and it can be determine by using arithmetic operations.
Arithmetic operations can be use to determine the error in the work shown. The steps to determine error are as follows:
Step 1 - Rewrite the expression.
[tex]\dfrac{1}{64}= 15^{2a}[/tex]
Step 2 - Write 64 as [tex]2^3[/tex].
[tex]\dfrac{1}{2^6} = 16^{2a}[/tex]
Step 3 - Write 16 as [tex]2^4[/tex]
[tex]\dfrac{1}{2^6} =(2^4)^{2a}[/tex]
Step 4 - Further simplify the above expression.
[tex]2^{-6}=2^{8a}[/tex]
Step 5 - Apply the same base property: [tex]a^b=a^c \Rightarrow b=c[/tex] .
-6 = 8a
[tex]a = \dfrac{-3}{4}[/tex]
Therefore, from the above steps it can be concluded that the error in the work shown is in the third step because in third step same base property is not apply correctly.
For more information, refer the link given below:
https://brainly.com/question/21835898
