Question

$( \frac{ { - 15}^{13} }{16} {)}^{ - 3 \div } (( \frac{15}{16} {)}^{ - 15 \times } ( \frac{ - 15}{16} {)}^{ - 5})$
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Answer 1

Answer:

$\frac{1}{(15)^{19}(16)^{17} }$

Step-by-step explanation:

$(\frac{-15^{13} }{16}) ^{-3}$ ÷ [$(\frac{15}{16})^{-15}$ x $(\frac{-15}{16})^{-5}$]

= $(\frac{-15^{13} }{16}) ^{-3}$ ÷ [$(\frac{15}{16})^{-15}$ x $(-1)^{-5} (\frac{15}{16})^{-5}$]

= $\frac{15^{-39} }{(-1)^{3} 16^{-3} }$ ÷ [$\frac{(\frac{15}{16})^{-20}}{(-1)^{5} }$ ]

= $-\frac{16^{3} }{15^{39} }$ ÷ [$\frac{(\frac{15}{16})^{-20}}{(-1) }$ ]

=  $-\frac{16^{3} }{15^{39} }$x $\frac{-1}{(\frac{15}{16})^{-20} }$

= $\frac{16^{3} }{15^{39} }$ x $(\frac{15}{16}) ^{20}$

= $\frac{1}{15^{(39-20)} 16^{(20-3)} }$

=$\frac{1}{(15)^{19}(16)^{17} }$