Question

Please help with these 2 problems

Answer 1

The expression can be simplified as follows:

$(\frac{16}{9})^{\frac{2}{3} }. (\frac{4}{3} ) ^{\frac{5}{3} } = \frac{16}{9}$  

4ˣ⁻¹ = 49 / 4

How to simplify an expression?

The expressions can be simplified as follows;

$(\frac{16}{9})^{\frac{2}{3} }. (\frac{4}{3} ) ^{\frac{5}{3} }$

Hence,

$(\frac{16}{9})^{\frac{2}{3} }. (\frac{4}{3} ) ^{\frac{5}{3} } = (\frac{4}{3} )^{2(\frac{2}{3} )}.(\frac{4}{3} ) ^{\frac{5}{3} }$

Therefore,

$(\frac{4}{3} )^{2(\frac{2}{3} )}.(\frac{4}{3} ) ^{\frac{5}{3} } = (\frac{4}{3} )^{\frac{4}{3} } .(\frac{4}{3} )^{\frac{5}{3} }$

Finally,

$(\frac{4}{3} )^{\frac{4}{3} } .(\frac{4}{3} )^{\frac{5}{3} } = (\frac{4}{3} )^{3}$

$(\frac{4}{3} )^{3} = \frac{16}{9}$

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

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

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