Sure! Let's simplify the given expression step-by-step:
The expression we have is
[tex]$
\frac{d^4}{d^6}
$[/tex]
To simplify this, we use the properties of exponents. Specifically, we use the rule that states:
[tex]$
\frac{a^m}{a^n} = a^{m-n}
$[/tex]
where [tex]\( a \)[/tex] is a base and [tex]\( m \)[/tex] and [tex]\( n \)[/tex] are exponents.
In this case, our base [tex]\( a \)[/tex] is [tex]\( d \)[/tex], [tex]\( m \)[/tex] is 4, and [tex]\( n \)[/tex] is 6. Applying the exponent rule, we subtract the exponent in the denominator from the exponent in the numerator:
[tex]$
d^{4-6}
$[/tex]
Simplify the exponent:
[tex]$
d^{-2}
$[/tex]
Therefore, the simplified form of the expression is:
[tex]$
d^{-2}
$[/tex]
Alternatively, you can also express this as a positive exponent:
[tex]$
\frac{1}{d^2}
$[/tex]
So the answer to the simplification is:
[tex]$
d^{-2}
$[/tex]
Answer: [tex]\( d^{-2} \)[/tex]
