Question

Which equation is equivalent to 16 Superscript 2 p Baseline = 32 Superscript p 3?.

Answer 1

The equation which is equivalent to 16 Superscript 2 p Baseline equal to 32 Superscript p 3 is,

$2^{8p}=2^{5p+15}$

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,

$16^{2p}=32^{p+3}$

Write both the equation in the form of same base number as,

$(2^4)^{2p}=(2^5)^{p+3}$

The power of the power of a number can be written as product of both the numbers. Thus,

$(2)^{4\times2p}=(2)^{5\times(p+3)}\\2^{8P}=2^{5P+15}$

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,

$8p=5p+15$

Solve it further to find the value of p as,

$8p-5p=15\\3p=15\\p=5$

Thus the equation which is equivalent to 16 Superscript 2 p Baseline equal to 32 Superscript p 3 is,

$2^{8p}=2^{5p+15}$

Learn more about the equivalent expression here;

brainly.com/question/2972832