Question

Which expressions are equivalent to 1.08^4t?

Answer 1

Answer:

Therefore,

The Equivalent expression is option A,

$(1.08^{4})^{t}$

Step-by-step explanation:

Given:

Expressions  is

$1.08^{4t}$

To Find:

Equivalent expression ?

Solution:

We have Law of indices

$(a^{x})^{y}=a^{x\times y}\\(a^{\frac {x}{y}})^{z}=a^{\frac{x\times z}{y}$

For option A

(1.08^t)^4

$(1.08^{4})^{t}=1.08^{4t}$

Hence option A is the Equivalent expression.

For option B

1.08^8t/1.08^2t

$(1.08^{\frac{8t}{1.08}})^{2t}=1.08^{\frac{16t^{2}}{1.08}}=1.08^{14.81t^{2}}$

Which is not the Equivalent expression.

For option C

1.08^4*1.08^t

$(1.08^{4\times 1.08})^{t}=1.08^{4.32t}$

Which is not the Equivalent expression.

For option D

1.08^6t/1.08^2t

$(1.08^{\frac{6t}{1.08}})^{2t}=1.08^{11.11t^{2}}$

Which is not the Equivalent expression.

Therefore,

The Equivalent expression is option A,

$(1.08^{4})^{t}$