Let's simplify the given expression step by step.
The expression provided is:
[tex]\[
\frac{b^{-3} c^0 d^2}{e^{-4}}
\][/tex]
### Step 1: Simplify [tex]\( c^0 \)[/tex]
Any non-zero number raised to the power of 0 is 1. Thus:
[tex]\[
c^0 = 1
\][/tex]
The expression simplifies to:
[tex]\[
\frac{b^{-3} \cdot 1 \cdot d^2}{e^{-4}} = \frac{b^{-3} d^2}{e^{-4}}
\][/tex]
### Step 2: Apply the rule for negative exponents
To simplify the expression, we use the rule for negative exponents: [tex]\( a^{-n} = \frac{1}{a^n} \)[/tex].
1. For [tex]\( b^{-3} \)[/tex]:
[tex]\[
b^{-3} = \frac{1}{b^3}
\][/tex]
2. For [tex]\( e^{-4} \)[/tex]:
[tex]\[
e^{-4} = \frac{1}{e^4}
\][/tex]
Since [tex]\( e^{-4} \)[/tex] is in the denominator, it becomes [tex]\( e^4 \)[/tex] in the numerator when simplified.
The expression now becomes:
[tex]\[
\frac{d^2}{b^3} \cdot e^4 = \frac{d^2 \cdot e^4}{b^3}
\][/tex]
### Step 3: Combine the results
Rewriting the simplified form properly, we have:
[tex]\[
\frac{d^2 \cdot e^4}{b^3}
\][/tex]
### Final Simplified Expression
The exponents should be clearly identified in the original problem statement:
[tex]\[
\frac{d^{[2]} e^{4}}{b^{3}}
\][/tex]
So, the exponents are [tex]\( d^{[2]} \)[/tex], [tex]\( e^{4} \)[/tex] and [tex]\( b^{3} \)[/tex] in the denominator.
