Question

Answer 1

c) \(\dfrac{10^{12}+5^{11}\cdot2^9-5^{13}\cdot2^8}{4\cdot5^5\cdot10^6}\)

\(=\dfrac{5^{12}\cdot2^{12}+5^{11}\cdot2^9-5^{13}\cdot2^8}{2^2\cdot5^5\cdot5^6\cdot2^6}\)

\(=\dfrac{5^{11}\cdot2^8\cdot\left(5\cdot2^4+1\cdot2-5^2\cdot1\right)}{5^{11}\cdot2^8}\)

\(=5\cdot2^4+2-5^2\)

\(=80+2-25\)

\(=57\)

Answer 2

\(=\dfrac{2^{12}\cdot5^{12}+5^{11}\cdot2^9-5^{13}\cdot2^8}{2^8\cdot5^{11}}=\dfrac{5^{11}\cdot2^8\left(2^4\cdot5+2-5^2\right)}{2^8\cdot5^{11}}\)

=80+2-25

=80-23

=57