Which of the following is developed to be equivalent to 1/8^5 ?(1 point)
Responses
8 1/5
8^−5
5^−8
8^5
To find an equivalent expression to 1/8^5, we need to find the reciprocal of 8^5.
The fifth power of 8 is represented by 8^5, so the reciprocal would be 1 divided by 8^5.
Therefore, the correct answer is 8^−5.
Which of the following is equivalent to 6^−2
?(1 point)
Responses
1/2^6
36
1/6^−2
1/36
To find an equivalent expression to 6^−2, we need to find the reciprocal of 6^2.
The square of 6 is represented by 6^2, so the reciprocal would be 1 divided by 6^2.
Therefore, the correct answer is 1/6^2.
Which of the following is an equivalent expression to 13^−5 ⋅13^−11
with only positive exponents, generated by applying the properties of exponents?(1 point)
Responses
1/26^6
1/26^16
1/13^16
1/13^6
To find an equivalent expression with only positive exponents, we can apply the property of exponents which states that when multiplying two numbers with the same base, we add their exponents.
So, 13^(-5) * 13^(-11) would be equivalent to 13^(-5 + -11) = 13^(-16).
Therefore, the correct answer is 1/13^16.
To find the expression equivalent to 1/8^5, we can apply the rule of exponents that states "if we have a negative exponent, it can be rewritten by taking the reciprocal of the base and making the exponent positive."
Therefore, let's rewrite 1/8^5 using this rule:
1/8^5 = 1/(1/8^5) = 8^(-5)
So, 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.
The exponent operator (^) indicates that the base, in this case, 8, should be raised to the power of the exponent, which is 5. So 8^5 can be expanded as 8 * 8 * 8 * 8 * 8, which equals 32,768.
To get the reciprocal of 32,768, we simply take 1 divided by 32,768.
Therefore, the equivalent value of 1/8^5 is 0.0000305176, which can be expressed in scientific notation as 3.05176 × 10^(-5).
Now let's check the given options:
1. 8 1/5: This option does not represent the equivalent value of 1/8^5.
2. 8^−5: This option represents the value of 8 raised to the power of -5. Since the exponent is negative, the value will be a fraction. However, it is not equivalent to 1/8^5.
3. 5^−8: This option represents the value of 5 raised to the power of -8. Again, this will result in a fraction, but it is not equivalent to 1/8^5.
4. 8^5: This option represents the value of 8 raised to the power of 5, which we have already determined to be 32,768. Since this is not the reciprocal of 1/8^5, it is not equivalent.
Therefore, none of the given options is equivalent to 1/8^5.