Question

Find the value 3 to the power minus 5 into 10 to the power minus 5 into 125 / 5 to the power minus 7 into 6 to the power minus 5

Answer 1

Answer:

$\bold{2^{-10} \times 3^{-10} \times 5^{-19}}$

Step-by-step explanation:

$3^{-5} \times 10^{-5} \times \left( \dfrac{125}{5} \right) ^{-7} \times 6^{-5}\\\\\\= 3^{-5} \times \left( 2 \times 5 \right) ^{-5} \times \left( 25 \right) ^{-7} \times \left( 2 \times 3 \right) ^{-5}\\\\= 3^{-5} \times 2^{-5} \times 5^{-5} \times \left( 5 \times 5 \right)^{-7} \times 2^{-5} \times 3^{-5}\\\\= 3^{-5} \times 2^{-5} \times 5^{-5} \times 5^{-7} \times 5 \right)^{-7} \times 2^{-5} \times 3^{-5}\\\\= 2^{-5 + (-5)} \times 3^{-5 + (-5)} \times 5^{-5 + (-7) + (-7)}$

$2^{-5-5} \times 3^{-5-5} \times 5^{-5-7-7}\\\\= \bold{2^{-10} \times 3^{-10} \times 5^{-19}}$