Question

Answer it please. Proper answer required

Answer 1

We're given,

→  a²bc³ = 25

→  ab² = 5

We have to find the value of abc.

All we have to do is just multiply the given both and then find the cube root. That's all!

First taking their product...

    a²bc³ × ab² = 25 × 5

⇒  a³b³c³ = 125

⇒  (abc)³ = 5³

Now taking the cube root, and we're done!

    abc = 5

Hence 5 is the answer.

Answer 2

Question :-

If a²bc³ = 25 and ab² = 5 then find the value of abc

Answer :-

abc = 5

Solution :-

a²bc³ = 25 ......(1)

ab² = 5 .....(2)

Multiply (2) with (1) on both sides

⇒ a²bc³(ab²) = 25(5)

⇒ a²(a) * b(b²) * c³ = 125

⇒ a²(a¹) * b¹(b²) * c³ = 125

$\sf \implies a^{2 + 1} \times b^{2 + 1} \times c^3 = 125$

$\bf \because a^{m} \times a^n = a^{mn}$

⇒ a³ * b³ * c³ = 125

⇒ (abc)³ = 125

$\bf \because a^{n} \times b^n = (ab)^{n}$

$\sf \implies abc = \sqrt[3]{125}$

$\sf \implies abc = \sqrt[3]{ {5}^{3} }$

$\sf \implies abc =5$

$\sf \therefore abc =5$

$\Huge{\boxed{ \sf abc = 5}}$

Laws of exponents used :-

$\tt \rightarrow a^{m} \times a^n = a^{mn}$

$\tt \rightarrow a^{n} \times b^n = (ab)^{n}$