Let's simplify the given expression step by step:
[tex]\[
\frac{b^{-3} c^0 d^2}{e^{-4}}
\][/tex]
1. Consider the term [tex]\(c^0\)[/tex]:
By the properties of exponents, any number raised to the power of 0 is 1. So, [tex]\(c^0 = 1\)[/tex]. This simplifies the expression to:
[tex]\[
\frac{b^{-3} \cdot 1 \cdot d^2}{e^{-4}} = \frac{b^{-3} d^2}{e^{-4}}
\][/tex]
2. Simplify [tex]\(e^{-4}\)[/tex] in the denominator:
An exponent of [tex]\(-4\)[/tex] in the denominator can be brought to the numerator by changing the sign of the exponent. This property tells us:
[tex]\[
e^{-4} = \frac{1}{e^4}
\][/tex]
Therefore,
[tex]\[
\frac{b^{-3} d^2}{e^{-4}} = b^{-3} d^2 \cdot e^4
\][/tex]
3. Combine all terms in the numerator:
Rewriting the expression with all terms in the numerator, we get:
[tex]\[
b^{-3} d^2 e^4
\][/tex]
4. Eliminate negative exponent [tex]\( b^{-3} \)[/tex]:
[tex]\( b^{-3} \)[/tex] in the numerator implies:
[tex]\[
b^{-3} = \frac{1}{b^3}
\][/tex]
Therefore,
[tex]\[
b^{-3} d^2 e^4 = \frac{d^2 e^4}{b^3}
\][/tex]
5. Converting above step to a fraction form:
After simplifying, we see the terms inside a fraction:
[tex]\[
\frac{d^2 e^4}{b^3}
\][/tex]
Hence, the final simplified expression is as follows:
[tex]\[
\frac{d^2 e^4}{b^3}
\][/tex]
In the final form:
[tex]\[
\frac{d^{[2]} e^{4}}{b^3}
\][/tex]
So the values are:
[tex]\[ d^{2} e^{4}, b^3 \][/tex]
which gives:
[tex]\[ (2, 4, 3) \][/tex]
Therefore, simplified result in the given expression is:
[tex]\[
\frac{d^2 e^4}{b^3}
\][/tex]
