Question

by what number should be (144/225)^-1 be divide so that the quotient may be equal to (12/15)^-4​

Answer 1

${ (\frac{144}{225}) }^{ - 1} \div x = { (\frac{12}{15}) }^{ - 4} \\ { (\frac{225}{144}) }^{1} \times \frac{1}{x} = {( \frac{15}{12} )}^{ 4} \\ \frac{25}{16} \times \frac{1}{x} = { (\frac{5}{4} )}^{4} \\ \frac{25}{16} \times { (\frac{4}{5}) }^{4} = x \\ \frac{25 \times 16 \times 16}{16 \times 25 \times 25} = x \\ \frac{16}{25} = x$