Question

Helpp.

Answer 1

\(\dfrac{14^{1005}\cdot5^{1006}}{2^{1007}\cdot35^{1004}}\)

\(=\dfrac{\left(2\cdot7\right)^{1005}\cdot5^{1006}}{2^{1007}\cdot\left(5\cdot7\right)^{1004}}\)

\(=\dfrac{2^{1005}\cdot5^{1006}\cdot7^{1005}}{2^{1007}\cdot5^{1004}\cdot7^{1004}}\)

\(=\dfrac{1}{2^2}\cdot5^2\cdot7=25\cdot\dfrac{7}{4}=\dfrac{175}{4}\)

Answer 2

\(4,\dfrac{14^{1005}.5^{1006}}{2^{1007}.35^{1004}}=\dfrac{\left(2.7\right)^{1005}.5^{1006}}{2^{1007}.\left(7.5\right)^{1004}}=\dfrac{2^{1005}.7^{1005}.5^{1006}}{2^{1007}.7^{1004}.5^{1004}}=\dfrac{7.5^2}{2^2}=\dfrac{7.25}{4}=\dfrac{175}{4}\)