Mathematics

Mathematics

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. a. (i) Simplify

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

to a single power of

t

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

E_5

completely and express it in the form

t^{k}

. c. (iii) State the value of

k

.

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