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Crazy boy [7]
3 years ago
15

(ar^b)^4=81r^24 where a and b are positive integers. Work out a and b

Mathematics
1 answer:
galina1969 [7]3 years ago
6 0

Answer:

Vales of a =3 and b = 6

Step-by-step explanation:

Given that: (ar^b)^4 = 81r^{24}            .....[1] where a and b are positive integers

we can write 81 and 24 as;

81 = 3 \cdot 3 \cdot 3 \cdot 3 = 3^4

24 = 4 \cdot 6

We have [1] as;

(ar^b)^4 = 3^4r^{4 \cdot 6}

Using power rules;

a^nb^n = (ab)^n

a^n = b^n which implies a = b

then;

(ar^b)^4 = (3r^6)^4

ar^b = 3r^6

On comparing both sides we have;

a = 3 and

r^b = r^6

⇒b = 6

Therefore, the value of a and b are, 3 and 6





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