Final answer:
To simplify the expression (-3)¹/³(-3)¹/³(-3)¹/³, take the cube root of each -3 term and multiply the results together. The simplified expression is -1.
Step-by-step explanation:
To simplify the expression (-3)¹/³(-3)¹/³(-3)¹/³, we first need to understand how to simplify expressions with fractional exponents. A fractional exponent represents the nth root of a number, where the denominator of the exponent represents the nth root and the numerator represents the exponent. In this case, the ¹/³ exponent means that we need to take the cube root of each -3 term.
The cube root of -3 is -1, so we can rewrite the expression as (-1)(-1)(-1). When multiplying negative numbers, we multiply the absolute values and then apply the negative sign if there are an odd number of negative factors. Since we have three negative factors, the result is -1.
Therefore, the simplified expression is -1.
The student has asked to simplify the expression (-3)¹⁄³(-3)¹⁄³(-3)¹⁄³. This involves applying the rule of exponentiation, specifically, the cubing of exponentials. According to the multiplication property of exponents, when we multiply exponential terms with the same base, we add their exponents. Here, each factor has the base of -3 and each exponent is 1/3. Adding these exponents, you get (1/3) + (1/3) + (1/3) = 1. Therefore, the expression simplifies to (-3)1, which is just -3.