Question

Which exponent makes the statement true: 1/5? = 9?
a) −2
b) −1
c) 1
d) 2

Answer 1

To determine which exponent makes the statement 1/5^x = 9 true, we must understand the properties of negative exponents. None of the given options a) -2, b) -1, c) 1, or d) 2 make the equation true, so the correct answer is 'None of the above'.

Step-by-step explanation:

The student is asking which exponent makes the equation 1/5x = 9 true. To solve this, we must think about the properties of negative exponents and try the options provided to see which one fits. We look for an exponent x such that when 5 is raised to that exponent and then inverted (because of the negative exponent), it equals 9.

Let's try the options given:

• a) -2: 1/5-2 = 52 = 25. This is not equal to 9.
• b) -1: 1/5-1 = 51 = 5. This is also not equal to 9.
• c) 1: 1/51 = 1/5, which is also not equal to 9.
• d) 2: 1/52 = 1/25, which is also not equal to 9.

Therefore, none of these options make the equation true, and the answer should be 'None of the above'.