Answer :
Answer:
[tex]\dfrac{1}{6^8}[/tex]
Step-by-step explanation:
[tex]\dfrac{6^{-3}}{6^5}=\dfrac{1}{6^{5+3}}=\dfrac{1}{6^8}[/tex]
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The applicable rules of exponents are ...
[tex]a^{-b}=\dfrac{1}{a^b}\\\\a^b\times a^c=a^{b+c}[/tex]
Answer:
The simplified expression is given by:
1 over 6 to the 8th power.
[tex]\dfrac{1}{6^8}[/tex]
Step-by-step explanation:
We are asked to simplify the expression:
6 to the negative 3rd power over 6 to the 5th power.
which is mathematically written as:
[tex]\dfrac{6^{-3}}{6^5}[/tex]
Now, we know that:
[tex]\dfrac{a^m}{a^n}=\dfrac{1}{a^{n-m}}[/tex]
Here,
[tex]m=-3\ and\ n=5[/tex]
Hence, we get:
[tex]\dfrac{6^{-3}}{6^5}=\dfrac{1}{6^{5-(-3)}}[/tex]
i.e.
[tex]\dfrac{6^{-3}}{6^5}=\dfrac{1}{6^{5+3}}[/tex]
Hence, we get the simplified expression as follows:
[tex]\dfrac{6^{-3}}{6^5}=\dfrac{1}{6^8}[/tex]