If (x^2a/x^4) =

[(square root of x^7)/x^a], what is the value of a?

To find the value of a in the equation, we can start by simplifying both sides of the equation.

Let's begin by simplifying the expression on the left-hand side (LHS):

(x^2a / x^4)

When dividing two variables with the same base, we subtract their exponents. So, subtracting the exponent of x in the denominator from the exponent of x in the numerator, we get:

x^(2a - 4)

Next, let's simplify the expression on the right-hand side (RHS):

[(square root of x^7) / x^a]

The square root of x^7 can be written as x^(7/2), since taking the square root is the same as raising the exponent to 1/2. Dividing by x^a, we subtract the exponents:

x^(7/2 - a)

Now, we can set the LHS equal to the RHS and compare the exponents:

x^(2a - 4) = x^(7/2 - a)

Since the bases (x) are the same, the exponents must be equal. Therefore, we can set the exponents equal to each other:

2a - 4 = 7/2 - a

Now, let's solve this equation for a.

First, let's isolate the term with "a" on one side by adding "a" to both sides:

2a + a - 4 = 7/2

Combining like terms:

3a - 4 = 7/2

Next, let's isolate the term with "a" by adding 4 to both sides:

3a = 7/2 + 4

Combining fractions:

3a = (7 + 8) / 2

3a = 15/2

Finally, let's solve for "a" by dividing both sides by 3:

a = (15/2) / 3

Dividing fractions:

a = (15/2) * (1/3)
a = 15/6
a = 5/2

Therefore, the value of a is 5/2.