108 = 3³ × 2²
Further explanation
Let's recall following formula about Exponents and Surds:
[tex]\boxed { \sqrt { x } = x ^ { \frac{1}{2} } }[/tex]
[tex]\boxed { (a ^ b) ^ c = a ^ { b . c } } [/tex]
[tex]\boxed {a ^ b \div a ^ c = a ^ { b - c } }[/tex]
[tex]\boxed {\log a + \log b = \log (a \times b) }[/tex]
[tex]\boxed {\log a - \log b = \log (a \div b) }[/tex]
Let us tackle the problem!
[tex]\texttt{ }[/tex]
[tex]108 = 54 \times 2[/tex]
[tex]108 = (27 \times 2) \times 2[/tex]
[tex]108 = (9 \times 3) \times 2 \times 2[/tex]
[tex]108 = (3 \times 3) \times 3 \times 2 \times 2[/tex]
[tex]108 = 3^3 \times 2^2[/tex]
[tex]\texttt{ }[/tex]
Conclusion:
The number 108 could be represented in expanded form and exponent as following:
[tex]\boxed{ 108 = 3^3 \times 2^2 }[/tex]
[tex]\texttt{ }[/tex]
Learn more
- Coefficient of A Square Root : https://brainly.com/question/11337634
- The Order of Operations : https://brainly.com/question/10821615
- Write 100,000 Using Exponents : https://brainly.com/question/2032116
Answer details
Grade: High School
Subject: Mathematics
Chapter: Exponents and Surds
Keywords: Power , Multiplication , Division , Exponent , Surd , Negative , Postive , Value , Equivalent , Perfect , Square , Factor.
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