Which of the following is developed to be equivalent to 1/8^5 (1 point)
5^-8
8^5
8^-5
8 1/5
The answer is 5^-8.
To find the equivalent expression to 1/8^5, we need to simplify the expression 1/8^5.
The expression 8^5 means "8 raised to the power of 5", which is equivalent to 8 * 8 * 8 * 8 * 8 = 32768. However, we want the reciprocal of this value, which is 1/32768.
Therefore, the correct answer is:
8^-5
To determine which of the options is equivalent to 1/8^5, we can simplify the equation step by step.
First, let's break down 1/8^5.
The exponent of 5 in 1/8^5 means that 8 should be raised to the power of 5. Since 1/8 is the reciprocal of 8, 1/8^5 can be rewritten as (1/8)^5.
Next, let's simplify (1/8)^5.
To calculate (1/8)^5, raise the numerator (1) to the power of 5, and raise the denominator (8) to the power of 5. Simplifying further, we have 1^5 / 8^5.
So, the expression 1/8^5 becomes 1/8^5 = 1^5 / 8^5
Since any number raised to the power of 1 is itself, 1^5 equals 1.
Thus, we have 1 / 8^5 = 1 / (8^5) = 1 / 32768.
Out of the given options:
- 5^-8 is equal to 1/5^8, which is not equivalent to 1/8^5.
- 8^5 is not equivalent to 1/8^5.
- 8^-5 is equal to 1/8^5.
Therefore, the correct option that is equivalent to 1/8^5 is 8^-5.