For , consider the expression E_5 = (t^ 1/2 )^ 4 , ,t^ -3 t^ -1/2 . Answer the…

MATHEMATICS · Multi-part · GCSE · Mathematics · Number · Number

Problem

For

t>0

, consider the expression

E_5 = \dfrac{\bigl(t^{1/2}\bigr)^{4}\,\cdot\,t^{-3}}{t^{-1/2}}.

Answer the following questions. (i) Simplify

(t^{1/2})^{4}

to a single power of

t

. (ii) Using the result of part (i), simplify

E_5

completely and express it in the form

t^{k}

. (iii) State the value of

k