Which of the following is developed to be equivalent to 185?(1 point)
Responses
5−8
5 superscript negative 8 baseline
8−5
8 superscript negative 5 baseline
815
8 Start Fraction 1 over 5 End Fraction
85
8 superscript 5 baseline
8-5
sure?
I apologize for the confusion. The correct answer is 8-5.
Which of the following is equivalent to 6−2?(1 point)
Responses
36
36
16−2
Start Fraction 1 over 6 superscript negative 2 baseline End Fraction
136
Start Fraction 1 over 36 End Fraction
126
6-2 is equivalent to 4. None of the given responses match the correct answer.
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
1266
Start Fraction 1 over 26 superscript 6 baseline end fraction
1136
Start Fraction 1 over 13 Superscript 6 baseline End Fraction
11316
Start Fraction 1 over 13 superscript 16 baseline end fraction
12616
Start Fraction 1 over 26 superscript 16 baseline end fraction
To find an equivalent expression with positive exponents, we can use the property of exponents that states: a^(-b) = 1/(a^b)
Applying this property to the given expression, we have:
13^(-5) * 13^(-11) = 1/(13^5) * 1/(13^11)
Thus, the equivalent expression with positive exponents is:
Start Fraction 1 over 13 Superscript 5 baseline End Fraction * Start Fraction 1 over 13 Superscript 11 baseline End Fraction
The correct response is: 1136
Which of the following is an equivalent expression to 14−79−13 with only positive exponents, generated by applying the Property of Negative Integer Exponents?(1 point)
Responses
1913 ⋅14−7
Start Fraction 1 over 9 superscript 13 baseline times 14 superscript negative 7 baseline End Fraction
14−7⋅913
14 superscript negative 7 baseline times 9 superscript 13 baseline
913147
Start Fraction 9 superscript 13 baseline over 14 superscript 7 baseline end fraction
147913
To apply the property of negative integer exponents, we can rewrite the expression as:
14^-7 * 9^-13
Using the property a^-b = 1/(a^b), we can rewrite it as:
1/(14^7) * 1/(9^13)
Therefore, the equivalent expression with only positive exponents is:
Start Fraction 1 over 14 Superscript 7 baseline End Fraction * Start Fraction 1 over 9 Superscript 13 baseline End Fraction
The correct response is: 1913 ⋅14−7
To determine which of the given options is equivalent to 185, we need to compare each option and see if any of them have the same value as 185.
Option 5−8:
To find the value of this expression, subtract 8 from 5:
5−8 = -3
Since -3 is not equal to 185, option 5−8 is not equivalent to 185.
Option 8−5:
To find the value of this expression, subtract 5 from 8:
8−5 = 3
Since 3 is not equal to 185, option 8−5 is not equivalent to 185.
Option 815:
This option is a mixed number written in the form of a fraction. To convert it to an improper fraction, multiply the whole number (8) by the denominator (5) and add the numerator (1) to get the new numerator. The denominator remains the same:
8 * 5 = 40
40 + 1 = 41
Therefore, this mixed number can be written as the improper fraction 41/5.
Since 41/5 is not equal to 185, option 815 is not equivalent to 185.
Option 85:
This is a number written as 8 raised to the power of 5.
Hence, 85 means 8 multiplied by itself 5 times:
85 = 8 * 8 * 8 * 8 * 8 = 32,768
Since 32,768 is not equal to 185, option 85 is not equivalent to 185.
After examining all the given options, none of them are equivalent to 185.