The equation which is equivalent to 16 Superscript 2 p Baseline equal to 32 Superscript p 3 is,
![2^{8p}=2^{5p+15}](https://tex.z-dn.net/?f=2%5E%7B8p%7D%3D2%5E%7B5p%2B15%7D)
<h3>What is equivalent equation?</h3>
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,
![16^{2p}=32^{p+3}](https://tex.z-dn.net/?f=16%5E%7B2p%7D%3D32%5E%7Bp%2B3%7D)
Write both the equation in the form of same base number as,
![(2^4)^{2p}=(2^5)^{p+3}](https://tex.z-dn.net/?f=%282%5E4%29%5E%7B2p%7D%3D%282%5E5%29%5E%7Bp%2B3%7D)
The power of the power of a number can be written as product of both the numbers. Thus,
![(2)^{4\times2p}=(2)^{5\times(p+3)}\\2^{8P}=2^{5P+15}](https://tex.z-dn.net/?f=%282%29%5E%7B4%5Ctimes2p%7D%3D%282%29%5E%7B5%5Ctimes%28p%2B3%29%7D%5C%5C2%5E%7B8P%7D%3D2%5E%7B5P%2B15%7D)
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,
![8p=5p+15](https://tex.z-dn.net/?f=8p%3D5p%2B15)
Solve it further to find the value of p as,
![8p-5p=15\\3p=15\\p=5](https://tex.z-dn.net/?f=8p-5p%3D15%5C%5C3p%3D15%5C%5Cp%3D5)
Thus the equation which is equivalent to 16 Superscript 2 p Baseline equal to 32 Superscript p 3 is,
![2^{8p}=2^{5p+15}](https://tex.z-dn.net/?f=2%5E%7B8p%7D%3D2%5E%7B5p%2B15%7D)
Learn more about the equivalent expression here;
brainly.com/question/2972832