Question

1. modeling real life a seed from an orchid has a mass of $10^{-6}$ gram. the mass of a seed from a double coconut palm is $10^{10}$ times the mass of the seed from the orchid. what is the mass of the seed from the double coconut palm in kilograms? ($1$ kg $= 10^3$ g)

Explanation:

Step1: Find the mass of the double coconut palm seed in grams.

The mass of the orchid seed is \(10^{-6}\) g, and the double coconut palm seed's mass is \(10^{10}\) times that. So we multiply: \(10^{-6} \times 10^{10}\). Using the rule of exponents \(a^m\times a^n = a^{m + n}\), we get \(10^{-6+10}=10^{4}\) g.

Step2: Convert grams to kilograms.

We know that \(1\) kg \( = 10^{3}\) g, so to convert grams to kilograms, we divide by \(10^{3}\). So we have \(\frac{10^{4}}{10^{3}}\). Using the rule of exponents \(\frac{a^m}{a^n}=a^{m - n}\), we get \(10^{4 - 3}=10^{1}=10\) kg.

Answer:

10