Question

Simplify $(5t^2{)}^2÷(25t{)}^{3/2}\times (5t^{1/2}{)}^3$ and find the power of $t$ to closest integer.

Answer 1

We have,

${\left(5t^2\right)}^2÷{\left(25t\right)}^{3/2}\times {\left(5t^{1/2}\right)}^3$

$\Rightarrow \left(5^2{t}^4\right)÷{\left(5^{2}t\right)}^{3/2}\times {\left(5t^{1/2}\right)}^3$

$\Rightarrow \left(5^2{t}^4\right)÷\left(5^3{t}^{3/2}\right)\times \left(5^3{t}^{3/2}\right)$

$\Rightarrow \left(5^2{t}^4\right)÷\left(5^6{t}^3\right)$

$\Rightarrow 5^{-4}t$

So, the power of $t$ is $1$.

Hence, this is the answer.