Respuesta :
The equation which is equivalent to 16 Superscript 2 p Baseline equal to 32 Superscript p 3 is,
[tex]2^{8p}=2^{5p+15}[/tex]
What is equivalent equation?
Equivalent equation are the expression whose result is equal to the original expression, but the way of representation is different.
Given information-
The given equation in the problem is,
[tex]16^{2p}=32^{p+3}[/tex]
Write both the equation in the form of same base number as,
[tex](2^4)^{2p}=(2^5)^{p+3}[/tex]
The power of the power of a number can be written as product of both the numbers. Thus,
[tex](2)^{4\times2p}=(2)^{5\times(p+3)}\\2^{8P}=2^{5P+15}[/tex]
This is the required equation.
Now if the base is the same at both side of the expression, then the powers can be compared. Thus,
[tex]8p=5p+15[/tex]
Solve it further to find the value of p as,
[tex]8p-5p=15\\3p=15\\p=5[/tex]
Thus the equation which is equivalent to 16 Superscript 2 p Baseline equal to 32 Superscript p 3 is,
[tex]2^{8p}=2^{5p+15}[/tex]
Learn more about the equivalent expression here;
https://brainly.com/question/2972832
