Which is the simplified form of [tex]m^{-8} p^0[/tex] ?
A. [tex]\frac{1}{m^8 p}[/tex]
B. [tex]\frac{1}{m^8}[/tex]
C. [tex]\frac{p}{m^8}[/tex]
D. [tex]m^8[/tex]
Answer (2)
Any non-zero number raised to the power of 0 is 1, so p 0 = 1 .
A negative exponent means taking the reciprocal, so m − 8 = m 8 1 .
Substitute the simplified terms back into the original expression: m − 8 p 0 = m 8 1 × 1 .
The simplified form of the expression is m 8 1 .
Explanation
Understanding the problem We are asked to simplify the expression m − 8 p 0 . To do this, we need to understand the rules of exponents, particularly how to handle negative exponents and exponents of zero.
Simplifying p^0 First, let's address the term p 0 . Any non-zero number raised to the power of 0 is equal to 1. Therefore, p 0 = 1 .
Simplifying m^-8 Next, let's simplify m − 8 . A negative exponent indicates that we should take the reciprocal of the base raised to the positive exponent. In other words, m − 8 = m 8 1 .
Combining the results Now, we substitute these simplified terms back into the original expression: m − 8 p 0 = m 8 1 × 1 = m 8 1 .
Final Answer Therefore, the simplified form of m − 8 p 0 is m 8 1 .
Examples
Understanding exponents is crucial in many fields, such as computer science and physics. For instance, in computer science, we use powers of 2 to represent memory sizes (e.g., kilobytes, megabytes, gigabytes). Simplifying expressions with exponents helps in calculating storage requirements or data transfer rates. In physics, exponential decay is used to model the decrease in radioactivity of a substance over time. Knowing how to manipulate exponents allows scientists to predict the remaining amount of a radioactive material after a certain period.
The simplified form of m − 8 p 0 is m 8 1 . Thus, the correct answer is option B: m 8 1 .
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