Respuesta :

The expression can be simplified as follows:

[tex](\frac{16}{9})^{\frac{2}{3} }. (\frac{4}{3} ) ^{\frac{5}{3} } = \frac{16}{9}[/tex]  

4ˣ⁻¹ = 49 / 4

How to simplify an expression?

The expressions can be simplified as follows;

[tex](\frac{16}{9})^{\frac{2}{3} }. (\frac{4}{3} ) ^{\frac{5}{3} }[/tex]

Hence,

[tex](\frac{16}{9})^{\frac{2}{3} }. (\frac{4}{3} ) ^{\frac{5}{3} } = (\frac{4}{3} )^{2(\frac{2}{3} )}.(\frac{4}{3} ) ^{\frac{5}{3} }[/tex]

Therefore,

[tex](\frac{4}{3} )^{2(\frac{2}{3} )}.(\frac{4}{3} ) ^{\frac{5}{3} } = (\frac{4}{3} )^{\frac{4}{3} } .(\frac{4}{3} )^{\frac{5}{3} }[/tex]

Finally,

[tex](\frac{4}{3} )^{\frac{4}{3} } .(\frac{4}{3} )^{\frac{5}{3} } = (\frac{4}{3} )^{3}[/tex]

[tex](\frac{4}{3} )^{3} = \frac{16}{9}[/tex]

2ˣ = 7

4ˣ⁻¹ = 2²⁽ˣ⁻¹⁾ = 2²ˣ ⁻ ²  = 2²ˣ / 2² = (2ˣ)² / 2²

Therefore,

(2ˣ)² / 2² = 7² / 2² = 49 / 4

Hence,

4ˣ⁻¹ = 49 / 4

Finally, the  [tex](\frac{16}{9})^{\frac{2}{3} }. (\frac{4}{3} ) ^{\frac{5}{3} }[/tex] is equal to [tex]\frac{16}{9}[/tex]  and for the second part  4ˣ⁻¹ = 49 / 4

learn more on simplification here: https://brainly.com/question/17513857

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