(7z^m)(nz^3)=-14z^7
solve for m and n
z^m z^3 = z^(m+3) = z^7
so m = 4
then n=-2
z^m * z^3 = z^7
7 * n = -14
To solve for m and n in the equation (7z^m)(nz^3) = -14z^7, we need to isolate each variable.
Let's begin by rewriting the equation without the exponent notation:
7zn^1 * z^3 * z^m = -14z^7
Using the laws of exponents, we can combine the terms with the same base (z) by adding their exponents:
7n * z^(1 + 3 + m) = -14z^7
Simplifying further:
7n * z^(4 + m) = -14z^7
To proceed, we'll equate the exponents on both sides of the equation:
4 + m = 7
By subtracting 4 from both sides of the equation, we get:
m = 7 - 4
m = 3
Now that we have the value of m, let's solve for n by equating the coefficients of z on both sides:
7n = -14
Divide both sides of the equation by 7:
n = -14/7
n = -2
Therefore, the solution for m is 3 and the solution for n is -2.
To solve for m and n, we need to simplify the equation by combining like terms and then equating the coefficients.
Let's start by simplifying the left side of the equation:
(7z^m)(nz^3) = 7n z^m z^3 = 7n z^(m+3)
Now, we can rewrite the equation as:
7n z^(m+3) = -14z^7
To proceed, we will equate the coefficients of the terms with the same power of z on both sides of the equation:
For the term with z^(m+3), the coefficient on the left side is 7n, and on the right side, it is -14.
Therefore, we have:
7n = -14
To solve for n, we divide both sides by 7:
n = -14/7
Simplifying further, we find:
n = -2
Now, let's equate the powers of z:
m + 3 = 7
To solve for m, we subtract 3 from both sides:
m = 7 - 3
m = 4
Therefore, the solution for m is 4 and n is -2.