Final answer:
To find the value of x in the equation 7^-2 * 3^2 = (3/4)^4x, we can simplify the left side of the equation and expand the right side. Cross multiplying and simplifying, we obtain the equation 9 * 2^8x = 49 * 3^4x. Equating the exponents, we solve for x to find x = 1/2.
Step-by-step explanation:
Given the expression 7-2 * 32 = (3/4)4x, we need to find the value of x.
To solve this, we can simplify the left side of the equation first. 7-2 means taking the reciprocal of 72, which is 1/72. 32 equals 9. So, the left side becomes (1/49) * 9.
Next, we can expand (3/4)4x by rewriting it as (34x) / (44x).
Now, equate the left and right sides of the equation and solve for x. (1/49) * 9 = (34x) / (44x).
Cross multiplying and simplifying, we get (1/49) * 9 * 44x = 34x.
By expressing 4 as 22, we can rewrite the equation as (1/49) * 9 * 28x = 34x.
Cancel out the common factors on both sides of the equation to obtain 9 * 28x = 49 * 34x.
Now, we can equate the exponents. 8x = 4x + 2.
Solving for x, subtract 4x from both sides of the equation to get 4x = 2.
Finally, divide both sides by 4 to find the value of x: x = 2/4 = 1/2.