Question

If (25ᵃ) (5)ᵃ⁺⁴ (125)²ᵃ = (625)¹⁰
Find a?

Answer 1

Step-by-step explanation:

5²ᵃ × 5ᵃ⁺⁴ × 5⁶ᵃ= 5⁴⁰

5⁹ᵃ⁺+⁴ = 5⁴⁰

9a+4 = 40

9a = 36

a= 4

Answer 2

⭐ Question :-

$\sf If\:(25^a)(5)^{a+4}(125)^{2a}=(625)^{10}, \\ \sf find \: the \: value \: of \: a.$

⭐ Solution :-

$\sf 25^a$ can be written as $\sf (5)^{2a}$

$\sf (125)^{2a}$ can be written as $\sf (5)^{6a}$

$\sf (625)^{10}$ can be written as $\sf (5)^{40}$

So, the law of exponents 1 : $\sf x^mx^n=x^{m+n}$

$\mapsto \sf 5^{2a}\:5^{a+4}\:5^{6a}=5^{40}$

$\mapsto \sf 2a+a+4+6a=40$

$\mapsto \sf 9a+4=40$

$\mapsto \sf 9a=40-4$

$\mapsto \sf a= \frac{\cancel{36}}{\cancel9}$

$\mapsto \sf a=4$

⭐Therefore, a = 4.

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All done :)