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 expression that is equivalent to 1/8^5, we need to apply the exponent rule for negative exponents, which states that any non-zero number raised to a negative exponent is equal to the reciprocal of that number raised to the positive exponent.
1/8^5 = (1/8)^5.
Therefore, the expression that is equivalent to 1/8^5 is (1/8)^5.
From the given options, none of them is equivalent to 1/8^5.
inncorect
Apologies for the incorrect response. Let's revisit the options:
1. 8^5: This expression represents 8 raised to the power of 5. It is not equivalent to 1/8^5.
2. 8 1/5: This expression represents 8 and one-fifth. It is not equivalent to 1/8^5.
3. 5^-8: This expression represents 5 raised to the power of negative 8. It is not equivalent to 1/8^5.
4. 8^-5: This expression represents 8 raised to the power of negative 5. It is equivalent to 1/8^5.
Therefore, the expression that is equivalent to 1/8^5 is 8^-5.
To determine which of the following is equivalent to 1/8^5, we need to simplify each expression and compare the results.
1. 8^5 = 8 * 8 * 8 * 8 * 8 = 32,768
2. 8 1/5 = 8 + 1/5 = 40/5 + 1/5 = 41/5
3. 5^-8 = 1/(5^8) = 1/390,625
4. 8^-5 = 1/(8^5) = 1/32,768
Comparing these results, we see that 1/8^5 is equivalent to 1/(8^5), which means the correct option is 8^-5.
To determine which of the given options is equivalent to 1/8^5, we need to simplify the expression 1/8^5.
To simplify this expression, we need to calculate the value of the base (8) raised to the power of the exponent (5). The exponent is negative, so we know that the value will be a fraction.
Option 1: 8^5
This option represents 8 raised to the power of 5. Since this does not involve any fraction, it is not equivalent to 1/8^5.
Option 2: 8 1/5
This option represents a mixed number, which is not equivalent to 1/8^5. It is denoting 8 plus 1/5.
Option 3: 5^-8
This option represents 5 raised to the power of -8. Since the base is different (5 instead of 8), it is not equivalent to 1/8^5.
Option 4: 8^-5
This option represents 8 raised to the power of -5. Since the base is the same as in 1/8^5, we can compare them.
Now, let's simplify the expression 1/8^5:
1/8^5 = 1/(8 × 8 × 8 × 8 × 8) = 1/32,768
Since 1/32,768 is equivalent to 1/8^5, the correct option is "8^-5."