bengalsfan0507 bengalsfan0507
  • 23-04-2019
  • Mathematics
contestada

Which of the following is equivalent to 5 square root 13^3
A.13^2
B.13^15
C.12^5/3
D.13^3/5

Respuesta :

carlosego
carlosego carlosego
  • 23-04-2019

For this case we must find an expression equivalent to the following:

[tex]5 \sqrt {13 ^ 3}[/tex]

By definition of properties of powers and roots we have:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

In addition, we know that:

[tex]13 ^ 3 = 13 ^ 2 * 13[/tex]

Rewriting the given expression we have:

[tex]5 \sqrt {13 ^ 3} = 5 \sqrt {13 ^ 2 * 13} = 13 * 5 \sqrt {13} = 65 \sqrt {13}[/tex]

Answer:

[tex]65 \sqrt {13}[/tex]

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