Respuesta :

Answer:

a = -4.

Step-by-step 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.

Kheazy

Answer:

[tex] - 4[/tex]

Step-by-step explanation:

[tex]25 \times { \sqrt{5} }^{a} \times { \sqrt{5} }^{3} = 5 \sqrt{5} [/tex]

[tex] {5}^{2} \times { \sqrt{5} }^{a} \times {5}^{3} = 5 \sqrt{5} [/tex]

But

[tex]5 = { \sqrt{5} }^{2} [/tex]

So,

[tex] { \sqrt{5} }^{4} \times { \sqrt{5} }^{a} \times { \sqrt{5} }^{3} = { \sqrt{5} }^{3} [/tex]

Eliminating |5,

[tex]4 + a + 3 = 3[/tex]

[tex]a = - 4[/tex]

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