Answer:
1) We can use the following property to simplify the product of powers as follows:
[tex]a^{m}\cdot a^{n} = a^{m + n}[/tex], [tex]a\in \mathbb{R}[/tex], [tex]m,n\in \mathbb{Z}[/tex] (1)
Therefore, we have the following result:
[tex]10^{12}\cdot 10^{0} = 10^{12+0} = 10^{12}[/tex]
A) [tex]10^{12}[/tex] must be multiplied either by [tex]10^{0}[/tex] or by [tex]1[/tex] to get the same answer.
Step-by-step explanation:
1) We can use the following property to simplify the product of powers as follows:
[tex]a^{m}\cdot a^{n} = a^{m + n}[/tex], [tex]a\in \mathbb{R}[/tex], [tex]m,n\in \mathbb{Z}[/tex] (1)
Therefore, we have the following result:
[tex]10^{12}\cdot 10^{0} = 10^{12+0} = 10^{12}[/tex]
A) In addition, we can use this property:
[tex]\frac{a^{m}}{a^{n}} = a^{m-n}[/tex], [tex]a\in \mathbb{R}[/tex], [tex]m,n\in \mathbb{Z}[/tex]
We can apply the property mentioned above:
[tex]10^{12}\cdot 10^{0} = 10^{12}\cdot (10^{n-n}) = 10^{12}\cdot \left(\frac{10^{n}}{10^{n}} \right) = 10^{12} \cdot 1 = 10^{12}[/tex]
In consequence, we conclude that [tex]10^{0} = 1[/tex]. [tex]10^{12}[/tex] must be multiplied either by [tex]10^{0}[/tex] or by [tex]1[/tex] to get the same answer.
