Which of the following is developed to be equivalent to 1/8^5
1. 5^-8
2. 8^-5
3. 8 1/5
4. 8^5
The correct option is 4. 8^5.
To solve 1/8^5, we can rewrite it as 8^-5.
To find the value equivalent to 1/8^5, we need to simplify 1/8^5 step by step.
1/8^5 is the same as 1/(8*8*8*8*8).
To simplify this further, we can rewrite 8 as 2^3 since 8 = 2*2*2.
So, 1/(8*8*8*8*8) becomes 1/(2^3 * 2^3 * 2^3 * 2^3 * 2^3).
Using the law of exponents, when we have the same base, we can add the exponents. Therefore, we can simplify the expression as 1/2^(3+3+3+3+3).
Adding the exponents, we get 1/2^15.
Hence, the answer is not listed among the options provided.
To find which of the following options is equivalent to 1/8^5, we need to simplify the expression 1/8^5.
1/8^5 can be rewritten as 1/(8^5).
To simplify this further, we can calculate the value of 8^5 using exponent rules.
8^5 = 8 * 8 * 8 * 8 * 8 = 32,768.
Therefore, 1/8^5 is equal to 1/32,768.
Now let's check which of the options is equivalent to this value:
1. 5^-8: This is equivalent to 1/5^8, which is not the same as 1/32,768.
2. 8^-5: This is equivalent to 1/8^5, which is indeed the same as 1/32,768.
3. 8 1/5: This is a mixed number and does not represent a power of 8. It is not equivalent to 1/32,768.
4. 8^5: This is equivalent to 8 * 8 * 8 * 8 * 8, which is not the same as 1/32,768.
Therefore, the option that is developed to be equivalent to 1/8^5 is option 2: 8^-5.