Answer with explanation:
Ques 1)
A)
We are given a expression as:
\(7x^{-8}\times 6x^3\)
It could also be written as:
\((7\times 6)\times x^{-8}\times x^3\\\\\\=42\times x^{-8+3}\\\\\\=42x^{-5}\\\\\\=\dfrac{42}{x^5}\)
Option: a is the answer.
B)
\((-2x^8)\times 3y^9\times 2x^4\)
which is solved as follows:
\((-2\times 3\times 2)\times x^8\times y^9\times x^4\\\\\\=-12x^{8+4}\times y^9\\\\\\=-12x^{12}y^9\)
Ques 2)
A)
The expression is:
\((8\times 10^7)(7\times 10^4)\)
It is solved as:
\(=(8\times 7)\times 10^7\times 10^4\\\\\\=56\times 10^{7+4}\\\\\\=56\times 10^{11}\\\\\\=5.6\times 10^{12}\)
Option: b is the answer.
B)
\((7\times 10^{-4})(9\times 10^{-10})\)
On simplifying:
\(=7\times 9\times 10^{-4}\times 10^{-10}\\\\\\=63\times 10^{-4-10}\\\\\\=63\times 10^{-14}\\\\\\=6.3\times 10^{-14+1}\\\\\\=6.3\times 10^{-13}\)
Option: a is the answer.
