(7z^ m )(nz ^ 3 )=−14z^7

To solve the given equation (7z^m)(nz^3) = -14z^7, we need to find the values of m and n.

First, let's simplify the left side of the equation by multiplying the coefficients and adding the exponents of the common base, which is 'z'.

7z^m * nz^3 = 7n * z^(m+3)

Now, we have the equation 7n * z^(m+3) = -14z^7.

To equate the exponents of 'z' on both sides, we set (m+3) = 7.

m + 3 = 7

Subtracting 3 from both sides, we get:

m = 7 - 3

m = 4

Now, we substitute the value of m back into the equation:

7n * z^(4+3) = -14z^7

7n * z^7 = -14z^7

Dividing both sides by z^7, we get:

7n = -14

Finally, solving for n:

n = -14/7

n = -2

Therefore, the values of m and n that satisfy the equation (7z^m)(nz^3) = -14z^7 are m = 4 and n = -2.

7n z^(m+3) = -14z^7

7n = -14
m+3 = 7