Question

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Answer 1

a = -4.

Explanation:

25(√5)^a * (√5) ^3 = 5√5

25*5^a/2 * 5^3/2 = 5*5^1/2

25*5^a/2 = 5*5^1/2 / 5^3/2

25*5^a/2 = 5^1 *5^1/2 / 5^3/2

25*5^a/2 = 5^3/2 / 5^3/2 = 1

5^a/2 = 1/25 = 5^-2

The bases are equal, so

a/2 = -2

a = -4.

Answer 2

`- 4`

Explanation:

`25 * { √(5) }^(a) * { √(5) }^(3) = 5 √(5)`

`{5}^(2) * { √(5) }^(a) * {5}^(3) = 5 √(5)`

But

`5 = { √(5) }^(2)`

So,

`{ √(5) }^(4) * { √(5) }^(a) * { √(5) }^(3) = { √(5) }^(3)`

Eliminating |5,

`4 + a + 3 = 3`

`a = - 4`