Let's address each question step by step:
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Which of the following is developed to be equivalent to 1 over 8^5? \[ 1 \div 8^5 = 8^{-5} \]
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Which of the following is equivalent to 6^-2? \[ 6^{-2} = \frac{1}{6^2} = \frac{1}{36} \]
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Which of the following is an equivalent expression to 13^-5*13^11 with only positive exponents? By applying the property of exponents \( a^m \cdot a^n = a^{m+n} \): \[ 13^{-5} \cdot 13^{11} = 13^{-5 + 11} = 13^{6} \]
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Which of the following is an equivalent expression to 14^-7 over 9^-13 with only positive exponents? Applying the properties of negative exponents: \[ \frac{14^{-7}}{9^{-13}} = \frac{1}{14^7} \cdot 9^{13} = \frac{9^{13}}{14^7} \]
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Which of the following is an equivalent expression to 7^3 over 25^-4 with only positive exponents? Using the properties of negative exponents: \[ \frac{7^3}{25^{-4}} = 7^3 \cdot 25^4 = 7^3 \cdot 25^4 \]
In summary, the answers are:
- \( 8^{-5} \)
- \( \frac{1}{36} \)
- \( 13^{6} \)
- \( \frac{9^{13}}{14^7} \)
- \( 7^3 \cdot 25^4 \)
1 answer