Answer:
[tex]a = 5[/tex]
[tex]b = - 3[/tex]
Step-by-step explanation:
Let set up the equation
[tex] {2}^{ - 3} \times {a}^{ - 3} = {10}^{b} [/tex]
First, let solve for a.
Since our product base is 10 and one of our factor base is 2. We need to find a number to multiply 2 by to get 10.
[tex]2 \times a = 10[/tex]
[tex]a = \frac{10}{2} [/tex]
[tex]a = 5[/tex]
Let replace a in the equation,
[tex] {2}^{ - 3} \times {5}^{ - 3} = {10}^{b} [/tex]
Using the rule that if two exponet have the same power but different bases, we multiply the bases and keep the same power.
We already multiplied the bases.
The power stay the same so b=-3
