Let's simplify the expression step by step:
The given expression is:
[tex]\[ 5^{-\frac{6}{2}} \cdot 5^{\frac{0}{2}} \][/tex]
Step 1: Simplify the exponents.
[tex]\[ -\frac{6}{2} = -3 \][/tex]
[tex]\[ \frac{0}{2} = 0 \][/tex]
Thus, the expression becomes:
[tex]\[ 5^{-3} \cdot 5^{0} \][/tex]
Step 2: Remember the property of exponents: [tex]\( a^m \cdot a^n = a^{m+n} \)[/tex]:
[tex]\[ 5^{-3} \cdot 5^{0} = 5^{-3+0} = 5^{-3} \][/tex]
Step 3: Simplify [tex]\( 5^{-3} \)[/tex]:
[tex]\[ 5^{-3} = \frac{1}{5^3} \][/tex]
[tex]\[ 5^3 = 5 \times 5 \times 5 = 125 \][/tex]
So,
[tex]\[ 5^{-3} = \frac{1}{125} \][/tex]
Combining all the steps, we get:
[tex]\[ 5^{-\frac{6}{2}} \cdot 5^{\frac{0}{2}} = \frac{1}{125} \][/tex]
Therefore, the correct answer is not among the given options. Based on numerical results:
[tex]\[(0.008, \cdot 1.0 = 0.008)\][/tex]
Thus, the result value is approximately [tex]\(\frac{1}{125} \approx 0.008\)[/tex].
