Question

simplify 3^-4*6^-3*25/10^-2*16*3^-6​

Answer 1

Step-by-step explanation:

what does the value of k so that the following system have a solution x-y-3z=3, 2x+z=0, 2y+7z=k

Answer 2

Step-by-step explanation:

${3}^{ - 4} \times {6}^{ - 3} \times \frac{25}{ {10}^{ - 2} } \times 16 \times {3}^{ - 6} \: \: use \: laws \: of \: exponents \:$

$= \frac{1}{ {3}^{4} } \times \frac{1}{ {6}^{3} } \times 25 \times {10}^{2} \times 16 \times \frac{1}{ {3}^{6} }$

$= \frac{1}{ {3}^{4} } \times \frac{1}{ {(2 \times 3)}^{3} } \times {5}^{2} \times {(2 \times 5)}^{2} \times {2}^{4} \times \frac{1}{ {3}^{6} }$

$= \frac{1}{ {3}^{4} } \times \frac{1}{ {2}^{3} \times {3}^{3} } \times {5}^{2} \times {2}^{2} \times {5}^{2} \times {2}^{4} \times \\ \frac{1}{ {3}^{6} } \\ = \frac{ {5}^{4} \times {2}^{3} }{ {3}^{13} }$