Which of the following is developed to be equivalent to 1/8^5?(1 point)
8^5
5−^8
8^1/5
8−^5
The correct option is: 5−^8
To find an expression equivalent to 1/8^5, we can rewrite it as (8^(-1))^5.
Now, we can apply the power rule which states that (a^m)^n is equal to a^(m*n).
Applying the power rule here, we get 8^(-1*5), which simplifies to 8^(-5).
Therefore, the expression equivalent to 1/8^5 is option D: 8^(-5).
To determine which of the given options is equivalent to 1/8^5, we need to understand how exponents work.
The expression 1/8^5 means that we have to take the fifth power of 8 in the denominator (8^5) and then calculate its reciprocal (1/).
Let's evaluate each option to see which one matches this criteria:
1) 8^5: This option is simply the fifth power of 8, which is not the reciprocal of it. Therefore, it is not equivalent to 1/8^5.
2) 5−^8: This option appears to have an incorrect formatting of the exponent. It should typically be written like 5^(-8) to represent the negative exponent. However, even if we assume it to be 5 to the power of negative 8, it is still not equivalent to 1/8^5.
3) 8^1/5: This option has an exponent of 1/5. If we interpret it as the fifth root of 8, it is not the reciprocal of 8^5. Therefore, it is not equivalent to 1/8^5 either.
4) 8−^5: Similar to option 2, this option seems to have a formatting error. Even if we assume it is 8 to the power of negative 5, it is still not equivalent to 1/8^5.
From the given options, none of them represent the reciprocal of 8^5. Therefore, the correct answer is none of the above.