The equivalent expression of [tex](2^ {-4} * z^ {-3} )^ 5[/tex] will be [tex]\frac{1}{(2^ {20} * z^ {15} )}[/tex], i.e. option C is the correct answer.
What is an expression?
Expression is a finite combination of symbols that is well-formed according to rules that depend on the context. An expression is a combination of numbers, variables, or a combination of numbers and variables, and symbols and it is connected by the sign of equal.
We have,
(2⁻⁴ × z⁻³)⁵ = ?
Now,
Using the exponent rule,
i.e.
(aⁿ)ᵇ = aⁿ ˣ ᵇ = aⁿᵇ
So,
(2⁻⁴ × z⁻³)⁵
i.e.
On solving,
We get,
(2⁻²⁰ × z⁻¹⁵)
Now,
Rewrite the above expression,
Using the exponent rule,
i.e.
[tex]\frac{1}{(2^ {20} * z^ {15} )}[/tex]
So,
(2⁻⁴ × z⁻³)⁵ = [tex]\frac{1}{(2^ {20} * z^ {15} )}[/tex]
I.e.
Option C is the correct answer for the expression (2⁻⁴ × z⁻³)⁵.
Hence, we can say that the equivalent expression of [tex](2^ {-4} * z^ {-3} )^ 5[/tex] will be [tex]\frac{1}{(2^ {20} * z^ {15} )}[/tex], i.e. option C is the correct answer.
To know more about expression click here
https://brainly.com/question/20055044
#SPJ2
