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BARSIC [14]
2 years ago
15

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

Mathematics
1 answer:
Juli2301 [7.4K]2 years ago
5 0

Answer:

n = 3

Step-by-step explanation:

Given:

The equation given is:

p^3q^2(p^4q^n\times \frac{r^3}{r^{-4}})=p^7q^5r^7

We simplify the given equation using the following law of indices:

a^m\times a^n=a^{m+n}\\\frac{a^m}{a^n}=a^{m-n}

Therefore,

p^{3+4}q^{n+2}\times r^{3-(-4)})=p^7q^5r^7\\p^7q^{n+2}r^7=p^7q^5r^7\\q^{n+2}=q^5

Since the base on both the sides is same, therefore, their exponents must also be same. This gives,

n+2=5\\n=5-2\\n=3

Therefore, the value of 'n' is 3.

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