Exponents -2

1. By what number should $(2/7)^{-2}$ be divided so that the quotient becomes 49?

Solution:

$$ \frac{(2/7)^{-2}}{x} = 49 \Rightarrow x = \frac{(2/7)^{-2}}{49} = 1 $$

2. Find x so that $(3/8)^{14} \times (8/3)^{-9} = (3/8)^{2x-1}$.

Solution:

$$ 14 - 9 = 2x - 1 \Rightarrow x = \frac{14 - 9 + 1}{2} = 3 $$

3. Find the value of a/b if $(a/b)^{-6}=(2/7)^{-6} \times (14/9)^{-6}$.

Solution:

$$ (a/b)^{-6} = (2/7)^{-6} \times (14/9)^{-6} \Rightarrow \frac{a}{b} = \frac{2 \times 14}{7 \times 9} = \frac{4}{3} $$

4. Simplify $(3^{-5} \times 10^{-5} \times 125) / (5^{-7} \times 6^{-5})$.

Solution:

$$ \frac{3^{-5} \times 10^{-5} \times 125}{5^{-7} \times 6^{-5}} = 6^5 \times 5^2 = 90000 $$

5. Mass of Earth is $5.97 \times 10^{24}$ kg and mass of Moon is $7.35 \times 10^{22}$ kg. What is the total mass?

Solution:

$$ 5.97 \times 10^{24} + 7.35 \times 10^{22} = 5.97 \times 10^{24} + 0.0735 \times 10^{24} = 6.0435 \times 10^{24} $$ kg