Please help me now.

SOLVE THE EXPONENTIAL EQUATION BELOW.
4(2^Xsquare)=8^X

If you mean

4(2^(x^2)) = 8^x
2^2 * 2^(x^2) = (2^3)^x
2^(2+x^2) = 2^(3x)
2+x^2 = 3x

I'm sure you can do that.

Next time you post one of these, try showing some of your work first, ok?

yeah! Thanks so much steve

To solve the exponential equation 4(2^(X^2)) = 8^X, we can start by simplifying the equation.

First, let's rewrite 8^X as (2^3)^X, using the property that 8 can be expressed as 2^3:

4(2^(X^2)) = (2^3)^X

Now, we can use the rule of exponents that says (a^m)^n = a^(m*n):

4(2^(X^2)) = 2^(3X)

Next, let's apply another rule of exponents, which states that if we have a power of a base raised to another exponent, we can multiply the exponents:

2^(2*X^2) = 2^(3X)

Since the bases are the same, we can equate the exponents:

2*X^2 = 3X

Now, we have a quadratic equation. Let's rearrange it by bringing all terms to one side:

2*X^2 - 3X = 0

To solve this quadratic equation, we can factor it or use the quadratic formula.

If we factor it, we would have:

X(2X - 3) = 0

Setting each factor equal to zero, we get:

X = 0 or 2X - 3 = 0

Solving for X in the second equation:

2X = 3
X = 3/2 or X = 1.5

So, the solutions to the exponential equation 4(2^(X^2)) = 8^X are X = 0, X = 1.5, and X = 3/2.