Which of the following is developed to be equivalent to 1/8^5
8^5
8 1/5
5^-8
8^-5
To find the equivalent expression to 1/8^5, we need to reciprocate the base and keep the exponent the same.
Therefore, the correct answer is 8^-5.
To find the expression that is equivalent to 1/8^5, we need to simplify it step by step.
First, let's simplify 8^5.
8^5 = 8 × 8 × 8 × 8 × 8 = 32768.
Next, let's simplify each of the remaining options:
Option 1: 8^5 is not equivalent to 1/8^5.
Option 2: 8 1/5 is equivalent to 8 + 1/5 = 8.2. This is not the same as 1/8^5.
Option 3: 5^-8 is equivalent to 1/5^8. When we simplify 1/5^8, we get 1/390625, which is not equal to 1/8^5.
Option 4: 8^-5 is equivalent to 1/8^5. This option is the correct answer and is equivalent to 1/32768.
Therefore, the expression that is equivalent to 1/8^5 is 8^-5.
To determine which of the options is equivalent to 1/8^5, let's break it down step by step:
Option 1: 8^5
This means raising 8 to the power of 5, which is equal to 8 × 8 × 8 × 8 × 8 = 32768.
Option 2: 8 1/5
This is not equivalent to 1/8^5. It represents a mixed fraction where the whole number is 8 and the fraction is 1/5.
Option 3: 5^-8
This means raising 5 to the power of -8. To solve this, we take the reciprocal of 5^8 (1/5^8), which is 1/390625.
Option 4: 8^-5
This means raising 8 to the power of -5. To solve this, we take the reciprocal of 8^5 (1/8^5), which is 1/32768.
Therefore, the correct answer is option 4, 8^-5, which is equivalent to 1/8^5.