Question

By what number should (5/4)power -3 be divided so that quotient may be (15/16)power -2

Answer 1

Step-by-step explanation:

$( \frac{5}{4} )^{ - 3} = ( \frac{4}{5})^{3} = \frac{64}{125}$

$( \frac{15}{16} )^{ - 2} = ( \frac{16}{15} )^{2} = \frac{256}{225}$

therefore,

$\frac{64}{125} \div x = \frac{256}{225}$

$x = \frac{256}{225} \times \frac{125}{64} = \frac{20}{9}$