Question

16) −3 4 × {( 9 25) 3 2 ÷ ( 5 2 ) −3 }

Answer 1

Answer:

(1681)4−3×[(259)23÷(25)−3]

=\left(\frac{3^{4}}{2^{4}}\right)^{\frac{-3}{4}}\times \left(\frac{2^{2}}{5^{2}}\right)^{\frac{3}{2}}\times \left(\frac{5}{2}\right)^{3}=(2434)4−3×(5222)23×(25)3

=\left(\frac{3}{2}\right)^{4\times\frac{-3}{4}}\times \left(\frac{3}{5}\right)^{2\times \frac{3}{2}}\times \left(\frac{5}{2}\right)^{3}=(23)4×4−3×(53)2×23×(25)3

=\left(\frac{2}{3}\right)^{3}\times \left(\frac{3}{5}\right)^{3}\times \left(\frac{5}{2}\right)^{3}=(32)3×(53)3×(25)3

=\left(\frac{2}{3}\times \frac{3}{5}\times \frac{5}{2}\right)^{3}=(32×53×25)3

=1^{3}=13

Therefore,

\left(\frac{81}{16}\right)^{\frac{-3}{4}}\times [\left(\frac{9}{25}\right)^{\frac{3}{2}}\div \left(\frac{5}{2}\right)^{-3}]=1(1681)4−3×[(259)23÷(25)−3]=1

Step-by-step explanation:

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