Respuesta :
Answer:
The simplest form is 128√2
Step-by-step explanation:
Let the expression be: [tex]8^{\frac{5}{2}}[/tex]
We know that a square root can also be written as a power of 1/2:
[tex]\sqrt{x} = x^\frac{1}{2}[/tex]
Simplify the given expression:
[tex]8^\frac{5}{2} = 8^{5\cdot\frac{1}{2}}[/tex]
write it in the square root form
[tex]8^{5\cdot\frac{1}{2}} = \sqrt{8^5}[/tex]
simplify the expression even further
[tex]\sqrt{8^5}= \sqrt{8^2\cdot8^2\cdot8} \\\sqrt{8^2\cdot8^2\cdot8} = \sqrt{8^2}\sqrt{8^2}\sqrt{8}[/tex]
where the terms with power 2 cancels the square root.
[tex]\sqrt{8^2} \sqrt{8^2} \sqrt{8} = 8\cdot8\cdot\sqrt{8} =64\sqrt{8} \\[/tex]
Simplify the expression under radical sign
[tex]64\sqrt{8} = 64\sqrt{2\cdot2\cdot2} \\64\sqrt{2\cdot2\cdot2} = 64\sqrt{2^2}\sqrt{2} \\64\sqrt{2^2}\sqrt{2} =64\cdot2\sqrt{2} \\64\cdot2\sqrt{2} =128\sqrt{2}[/tex]
The simplest form of the given expression [tex]8 ^{5/2}[/tex]is 128√2.
What is a simplification of an expression?
Usually, simplification involves proceeding with the pending operations in the expression.
Simplification usually involves making the expression simple and easy to use later.
Let the expression be:
[tex]8 ^{5/2}[/tex]
We know that a square root can also be written as a power of 1/2:
[tex]\sqrt{x} = x^{1/2}[/tex]
Simplify the given expression:
[tex]8^{5/2} = 8^{5.1/2}[/tex]
simplify the expression even further
[tex]\sqrt{8^5} = \sqrt{8^2.8^2.8}[/tex]
[tex]\sqrt{8^2} \sqrt{8^2} \sqrt{8} = 8 . 8. \sqrt{8} \\\\64\sqrt{8}[/tex]
Simplify the expression under the radical sign
[tex]64\sqrt{8} = 64 \sqrt{2} \sqrt{2} \sqrt{2} \\\\= 64. 2\sqrt{2} \\\\= 128 \sqrt{2}[/tex]
Learn more about expression;
https://brainly.com/question/2753269
#SPJ5
