Question

Simplify and write the answer in the exponential form
$-3^4\times {\left(\frac{5}{3}\right)}^4$
[3 marks]

Answer 1

$-3^4\times {\left(\frac{5}{3}\right)}^4={\left(-1\times 3\right)}^4\times \left(\frac{5^4}{3^4}\right)\Rightarrow -3^4\times {\left(\frac{5}{3}\right)}^4=\left({(-1)}^4\times {\left(3\right)}^4\right]\times \left(\frac{5^4}{3^4}\right)\Rightarrow -3^4\times {\left(\frac{5}{3}\right)}^4=(-1{)}^4\times {\left(3\right)}^4\times \frac{\left(}{5^4}[2\mathrm{marks}]\Rightarrow -3^4\times {\left(\frac{5}{3}\right)}^4=(-1{)}^4\times {\left(5\right)}^4\mathrm{as}(-1{)}^4=1,\mathrm{so}\Rightarrow -3^4\times {\left(\frac{5}{3}\right)}^4={\left(5\right)}^4[1\mathrm{mark}]$