Fully simplify and write your answer in exponential form with positive exponents only. Example: 153\frac{1}{5^3}
5
3
1
not 5−35^{-3}5
−3
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8−3⋅8⋅8−5=8^{-3}\cdot8\cdot8^{-5}=8
−3
⋅8⋅8
−5
=
To simplify the expression 8^{-3}\cdot8\cdot8^{-5}, we can use the property of exponents that states: a^{-m} = \frac{1}{a^m}.
Applying this property, we have:
8^{-3}\cdot8\cdot8^{-5} = \frac{1}{8^3}\cdot8\cdot\frac{1}{8^5} = \frac{1}{8^3\cdot8\cdot8^5}
Now, using the property of exponents that states: a^m\cdot a^n = a^{m+n}, we can simplify the denominator:
\frac{1}{8^3\cdot8\cdot8^5} = \frac{1}{8^{3+1+5}} = \frac{1}{8^9}.
Therefore, the fully simplified form of the expression is 8^{-3}\cdot8\cdot8^{-5} = \frac{1}{8^9}.