cbrelax wrote:
If \(\frac{(0.00000016 * 10^m) }{ (800 * 10^{-5})} = 0.02 * 10^{14}\), what is the value of m?
A. 15
B. 16
C. 17
D. 18
E.19
Given: \(\frac{0.00000016 * 10^m }{ 800 * 10^{-5}} = 0.02 * 10^{14}\)
Multiply both sides of the equation by \(800\) to get: \(\frac{0.00000016 * 10^m }{ 10^{-5}} = 16 * 10^{14}\)
Rewrite \(0.00000016\) as \(16 * 10^{-8}\) to get: \(\frac{16 * 10^{-8} * 10^m }{ 10^{-5}} = 16 * 10^{14}\)
Divide both sides by \(16\) to get: \(\frac{10^{-8} * 10^m }{ 10^{-5}} = 10^{14}\)
Multiply both sides by \(10^{-5}\) to get: \(10^{-8} * 10^m = 10^{9}\)
Divide both sides by \(10^{-8}\) to get: \(10^m = 10^{17}\)
Since the bases are equal, we know that the exponents are equal.
So, \(m = 17\)
Answer: C