Answer:
Therefore,
The Equivalent expression is option A,
[tex](1.08^{4})^{t}[/tex]
Step-by-step explanation:
Given:
Expressions is
[tex]1.08^{4t}[/tex]
To Find:
Equivalent expression ?
Solution:
We have Law of indices
[tex](a^{x})^{y}=a^{x\times y}\\(a^{\frac {x}{y}})^{z}=a^{\frac{x\times z}{y}[/tex]
For option A
(1.08^t)^4
[tex](1.08^{4})^{t}=1.08^{4t}[/tex]
Hence option A is the Equivalent expression.
For option B
1.08^8t/1.08^2t
[tex](1.08^{\frac{8t}{1.08}})^{2t}=1.08^{\frac{16t^{2}}{1.08}}=1.08^{14.81t^{2}}[/tex]
Which is not the Equivalent expression.
For option C
1.08^4*1.08^t
[tex](1.08^{4\times 1.08})^{t}=1.08^{4.32t}[/tex]
Which is not the Equivalent expression.
For option D
1.08^6t/1.08^2t
[tex](1.08^{\frac{6t}{1.08}})^{2t}=1.08^{11.11t^{2}}[/tex]
Which is not the Equivalent expression.
Therefore,
The Equivalent expression is option A,
[tex](1.08^{4})^{t}[/tex]
