Simplify and write each variable as an expression with positive exponents:
((-24x^9)/(8b^7))^4 = c((x^m)/(b^n))
To simplify and write each variable as an expression with positive exponents, we can start by simplifying the term on the left side of the equation, ((-24x^9)/(8b^7))^4.
Let's break it down step by step:
Step 1: Simplify the numerator and the denominator separately.
The numerator, -24x^9, can be simplified by dividing -24 by 8, which gives us -3. Additionally, we can rewrite x^9 as (x^8) * x, which gives us (-3x^8) * x = -3x^9.
The denominator, 8b^7, remains the same.
So, ((-24x^9)/(8b^7))^4 simplifies to ((-3x^9)/(b^7))^4.
Step 2: Apply the exponent to both the numerator and the denominator.
When raising a fraction to a power, we raise both the numerator and the denominator to that power.
((-3x^9)/(b^7))^4 simplifies to (-3^4 * (x^9)^4) / (b^7)^4.
Step 3: Simplify the exponents.
(-3^4 * (x^9)^4) / (b^7)^4 becomes (-3^4 * x^(9*4)) / b^(7*4).
(-3^4 * x^(9*4)) can be further simplified as (-81 * x^36).
Therefore, the left side of the equation simplifies to (-81 * x^36) / b^(7*4).
Now let's focus on the right side of the equation, c((x^m)/(b^n)).
The variables on the right side of the equation have variables x and b with exponents m and n, respectively.
So, the simplified expression is:
(-81 * x^36) / b^(7*4) = c((x^m)/(b^n))
Note that the values of m and n are not specified in the given equation, so we cannot determine their exact values based on the information provided.