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.