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Which of these is correct?(1 point)

Responses

676−5=36
the fraction with numerator 6 to the 7th power and denominator 6 to the negative 5 power is equal to 36

5856=25
the fraction with numerator 5 to the 8th power and denominator 5 to the 6th power is equal to 25

4043=0
the fraction with numerator 4 to the 0 power and denominator 4 cubed is equal to 0

3634=19
the fraction with numerator 3 to the 6th power and denominator 3 to the 4th power is equal to 1 ninth
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1 answer

Let's analyze each statement one by one to determine which is correct:

  1. 676−5=36

    • This statement seems to imply \( 6^{7-5} = 6^2 = 36 \). This statement is correct.

  2. 5856=25

    • This statement implies \( \frac{5^8}{5^6} = 5^{8-6} = 5^2 = 25 \). This statement is correct.

  3. 4043=0

    • This statement implies \( \frac{4^0}{4^3} = \frac{1}{4^3} = \frac{1}{64} \), not 0. This statement is incorrect.

  4. 3634=19

    • This statement implies \( \frac{3^6}{3^4} = 3^{6-4} = 3^2 = 9 \), not \( \frac{1}{9} \) or 19. This statement is incorrect.

Based on this evaluation, the correct responses are statements 1 and 2. However, since you are asking for one correct statement from the options given:

The correct response is:

  • 5856=25 (the fraction with numerator 5 to the 8th power and denominator 5 to the 6th power is equal to 25)