Question

Simplify simplify simplify simplify simplify

3^-5*10^-5*125/5^-7*6^-5​

Answer 1

Answer:

5^5 or 3125

Step-by-step explanation:

3^-5 * 10^-5 * 125 / 5^-7 * 6^-5

= 3^-5 * (2*5)^-5 * 5^3 / 5^-7 * (2*3)^-5

= 3^-5 * 2^-5 * 5^-5 * 5^3 / 5^-7 * 2^-5 * 3^-5

= 3^-5/ 3^-5 * 2^-5/ 2^ -5. * 5^-5* 5^3/ 5^-7

= 3^( -5+5) * 2^( -5+5) * 5^(-5+3+7)

= 3^0.* 2^0 * 5^5

= 1 * 1 * 5^5

= 5^ 5

= 3125

Answer 2

Answer:

$\frac{ {3}^{ - 5} \times {10}^{ - 5} \times 125}{ {5}^{ - 7} \times {6}^{ - 5} } \\ \\ = \frac{ {5}^{7} \times {6}^{5} \times 125 }{ {3}^{5} \times {10}^{5} } \\ \\ = \frac{ {5}^{7} \times {(3 \times 2)}^{5} \times {5}^{3} }{ {3}^{5} \times {(5 \times 2)}^{5} } \\ \\ = \frac{ {5}^{7} \times {3}^{5} \times {2}^{5} \times {5}^{3} }{ {3}^{5} \times {5}^{5} \times {2}^{5} } \\ \\ = \frac{ {(5)}^{7 + 3} \times {3}^{5} \times {2}^{5} }{ {3}^{5} \times {5}^{5} \times {2}^{5} } \\ \\ = \frac{ {5}^{10} \times {3}^{5} \times {2}^{5} }{{3}^{5} \times {5}^{5} \times {2}^{5}} \\ \\ = {(5)}^{10 - 5} \times {(3)}^{5 - 5} \times {(2)}^{5 - 5} \\ \\ = {5}^{5} \times {3}^{0} \times {2}^{0} \\ \\ = {5}^{5} \times 1 \times 1 \\ \\ \boxed{ = \underline{ \underline{ {5}^{5} }}}$