Here are the essential concepts you must grasp in order to answer the question correctly.
Exponents and Powers
Exponents represent repeated multiplication of a number by itself. In the expression 0.2^2/3, the exponent indicates that 0.2 is multiplied by itself two-thirds of a time, which can be interpreted as taking the square root of 0.2 squared. Understanding how to manipulate exponents is crucial for simplifying expressions involving powers.
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Fractional Exponents
Fractional exponents indicate both a power and a root. For example, an exponent of 2/3 means to square the base and then take the cube root of the result. This concept is essential for evaluating expressions like 40^2/3, as it allows for the simplification of calculations by breaking them into manageable steps.
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Order of Operations
The order of operations is a set of rules that dictates the sequence in which mathematical operations should be performed to ensure consistent results. The acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. Applying these rules correctly is vital for accurately calculating expressions like (0.2^2/3)(40^2/3).
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Performing Row Operations on Matrices