%5E3.jpeg "(10^-2)^3")
Understanding (10^-2)^3
This expression involves both exponents and parentheses. To solve it, we need to follow the order of operations (PEMDAS/BODMAS) which dictates that we should perform operations inside the parentheses first.
Breaking Down the Expression
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(10^-2): This part represents 10 raised to the power of -2. Remember that a negative exponent indicates the reciprocal of the base raised to the positive version of the exponent. Therefore:
- 10^-2 = 1/(10^2) = 1/100
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(10^-2)^3: Now, we have (1/100) raised to the power of 3. This means we multiply (1/100) by itself three times.
Calculation
(1/100)^3 = (1/100) * (1/100) * (1/100) = 1/1,000,000
Result
Therefore, (10^-2)^3 is equal to 1/1,000,000 or 10^-6.
Key Points
- Exponents: The power to which a number is raised (in this case, -2 and 3).
- Parentheses: Indicate the order of operations, ensuring calculations within them are done first.
- Negative Exponents: Indicate the reciprocal of the base raised to the positive version of the exponent.
By understanding these principles, we can confidently solve expressions involving exponents and parentheses.