Question

if p and q are whole numbers
$p^q=529, find [{{(6-q)^{p - 17} }}]^{ - 1}$
​

Answer 1

Have a great day ahead!!!!!!

Answer 2

Step-by-step explanation:

${p}^{q} = 529 \\ \\ = > {23}^{2} = 529 \\ \\ p = 23 \: \: and \: \: q = 2 \\ \\ ( {(6 - q)}^{p - 17} ) {}^{ - 1} \\ \\ = ((6 - 2) {}^{23 - 17} ) {}^{ - 1} \\ \\ = ((4) {}^{6} ) {}^{ - 1} \\ \\ = 4 {}^{ - 6} \\ \\ = \frac{1}{ {4}^{6} } \\ \\ p \: and \: q \: are \: whole \: number \: \: so \: \\ \\ ( { - 23})^{2} = 529 \\ \\ here \: p \: = - 23 \: and \: q \: = 2 \\ \\ (( {6 - q})^{p - 17} ) {}^{ - 1} \\ \\ = ((6 - 2) {}^{ - 23 - 17} ) {}^{ - 1} \\ \\ = ((4) {}^{ - 40} ) {}^{ - 1} \\ \\ = {4}^{40} \\ \\ \\ using \: formula \: \: ( {x}^{m} ) {}^{n} = {x}^{mn} \\ \\ {x}^{ - 1} = \frac{1}{x} \\ \\ {x}^{ - 2} = \frac{1}{ {x}^{2} }$