Which of the following is developed to be equivalent to 185?(1 point)
Responses
8^1/5
8 Start Fraction 1 over 5 End Fraction
5^−8
5 superscript negative 8 baseline
8^5
8 superscript 5 baseline
8^−5
8^5
To find out which of the following is equivalent to 185, we can evaluate each expression:
1. 8^1/5: This expression represents the fifth root of 8. To calculate this, raise 8 to the power of 1/5.
8^1/5 ≈ 1.515
2. 5^−8: This expression represents the reciprocal of 5 raised to the power of 8. To calculate this, raise 5 to the power of -8.
5^−8 ≈ 0.000000032
3. 8^5: This expression represents 8 raised to the power of 5.
8^5 = 32,768
4. 8^−5: This expression represents the reciprocal of 8 raised to the power of 5. To calculate this, raise 8 to the power of -5.
8^−5 ≈ 0.00003052
Based on these calculations, none of the given expressions is equivalent to 185.
To determine which of the given options is equivalent to 185, we need to evaluate each option.
Let's evaluate each option step-by-step:
1. Option 1: 8^1/5
To solve this, we need to find the fifth root of 8.
The fifth root of 8 is approximately 1.68.
2. Option 2: 5^−8
To solve this, we need to find the reciprocal power of 5 raised to the power of -8.
Reciprocal of 5^8 is 1/5^8 or 1/390,625.
3. Option 3: 8^5
To solve this, we need to raise 8 to the power of 5.
8^5 is equal to 32,768.
4. Option 4: 8^−5
To solve this, we need to find the reciprocal power of 8 raised to the power of -5.
Reciprocal of 8^5 is 1/8^5 or 1/32,768.
From the given options, the only option that is equivalent to 185 is Option 3: 8^5.