Find the value of n in the equation below.

Question

P^3 x q^2 ( p^4 x q^n x r^3/r^-4)= p^7 q^5 r^7

N=

Answer 1

To find the value of n, we need to equate the exponents of each base on both sides of the equation.

On the left side of the equation:
P^3 x q^2 ( p^4 x q^n x r^3/r^-4)

The exponent of P on the left side is 3, while on the right side, it is 7. Therefore, we have the equation: 3 = 7.

The exponent of q on the left side is 2 + n, while on the right side, it is 5. Therefore, we have the equation: 2 + n = 5.

The exponent of r on the left side is 3 - (-4), which simplifies to 3 + 4 = 7. On the right side, the exponent of r is already 7. Therefore, we don't need to equate the exponents of r.

Solving the equation 2 + n = 5 for n, we subtract 2 from both sides:
n = 5 - 2 = 3.

Therefore, the value of n is 3.