# How do you find w(t^2) given w(t)=t^2-5 ?

Jun 28, 2017

$w \left({t}^{2}\right) = {t}^{4} - 5$

#### Explanation:

If the question was find $w \left(3\right)$, we would replace $t$ with 3 and compute:

$w \left(3\right) = {3}^{2} - 5$

$w \left(3\right) = 9 - 5$

$w \left(3\right) = 4$

In this case, let's replace $t$ with ${t}^{2}$:

$w \left({t}^{2}\right) = {\left({t}^{2}\right)}^{2} - 5$

Using the exponential law:

${\left({a}^{m}\right)}^{n} = {a}^{m n}$

$w \left({t}^{2}\right) = {t}^{4} - 5$