To determine which option represents an equivalent expression with positive exponents generated by applying the properties of integer exponents, we need to analyze each option.
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~・（-4）: This expression does not clearly correspond to a change in exponents or provide context for exponentiation.
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(-4)*: The asterisk here might suggest a multiplication or it could be an incomplete representation of an operation. Alone, it does not indicate any exponent expression.
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⅔ 0: The expression \( a^0 = 1 \) for any non-zero \( a \) implies that \( \frac{2}{3}^0 = 1 \). This is using the property that any non-zero number raised to the power of 0 equals 1, resulting in a positive exponent outcome.
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（-4｝: Similar to the first option, this expression does not clearly indicate the use of exponential properties nor does it lead to clarity about positive exponents.
From this analysis, the correct equivalent expression using positive exponents is ⅔ 0, since it reflects the property of exponents that states any non-zero number raised to the zero power equals one.
7 answers