Which of the following is developed to be equivalent to 185?(1 point)
Responses
8^−5
8 superscript negative 5 baseline
8^5
8 superscript 5 baseline
5^−8
5 superscript negative 8 baseline
8 1/5
None of the above options are equivalent to 185.
Which of the following is developed to be equivalent to 1/8^5?(1 point)
Responses
8^−5
8 superscript negative 5 baseline
8^5
8 superscript 5 baseline
5^−8
5 superscript negative 8 baseline
8 1/5
The correct response is 8^(-5).
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
1/26^16
Start Fraction 1 over 26 superscript 16 baseline end fraction
1/26^6
Start Fraction 1 over 26 superscript 6 baseline end fraction
1/13^6
Start Fraction 1 over 13 Superscript 6 baseline End Fraction
1/13^16
To find an equivalent expression with only positive exponents, we can apply the property of exponents that states a^(-n) is equal to 1/a^n.
Using this property, the expression 13^(-5) can be rewritten as 1/(13^5), and the expression 13^(-11) can be rewritten as 1/(13^11).
So, the equivalent expression is (1/(13^5)) * (1/(13^11)).
By multiplying these fractions together, we get 1/(13^5 * 13^11).
Using the property of exponents that states a^m * a^n = a^(m+n), we can simplify the expression to 1/13^(5+11).
Therefore, the correct response is 1/13^16.
Which of the following is an equivalent expression to 14^−7/9^−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
913147
Start Fraction 9 superscript 13 baseline over 14 superscript 7 baseline end fraction
14−7⋅913
14 superscript negative 7 baseline times 9 superscript 13 baseline
147913
To find an equivalent expression with only positive exponents, we can apply the property of negative integer exponents, which states that a^(-n) is equal to 1/a^n.
Using this property, the expression 14^(-7) can be rewritten as 1/(14^7), and the expression 9^(-13) can be rewritten as 1/(9^13).
So, the equivalent expression is (1/(14^7)) * (1/(9^13)).
By multiplying these fractions together, we get 1/(14^7 * 9^13).
We do not have to simplify this expression any further as it is already written with only positive exponents.
Therefore, the correct response is 1/(14^7 * 9^13), which is equivalent to start fraction 1 over 14 superscript 7 baseline times 9 superscript 13 baseline end fraction.
Which of the following is an equivalent expression to 7^3/25^−4 with only positive exponents, generated by applying the Property of Negative Integer Exponents?(1 point)
Responses
2547−3
Start Fraction 25 superscript 4 baseline over 7 negative cubed end fraction
73⋅254
7 cubed times 25 superscript 4 baseline
73254
Start Fraction 7 cubed over 25 superscript 4 baseline end fraction
25473
To find an equivalent expression with only positive exponents, we can apply the property of negative integer exponents, which states that a^(-n) is equal to 1/a^n.
Using this property, the expression 25^(-4) can be rewritten as 1/(25^4), and the expression 7^3 can remain as is.
So, the equivalent expression is (7^3) * (1/(25^4)).
By multiplying these terms together, we get (7^3)/(25^4).
Therefore, the correct response is (7^3)/(25^4), which is equivalent to the option "73254".
To determine which of the given options is equivalent to 185, we can evaluate each option and compare the results:
1. 8^(-5): This means 8 raised to the power of -5. To evaluate this, we can use the exponentiation rule that states any number raised to the power of -n is equal to 1 divided by the number raised to the power of n. So, 8^(-5) = 1 / 8^5.
2. 8^5: This means 8 raised to the power of 5. To evaluate this, we multiply 8 by itself five times: 8^5 = 8 * 8 * 8 * 8 * 8 = 32768.
3. 5^(-8): This means 5 raised to the power of -8. Similar to the first option, we can apply the exponentiation rule to get 5^(-8) = 1 / 5^8.
4. 8 1/5: This is a mixed number, which can also be written as an improper fraction. To convert it, we multiply the whole number (8) by the denominator (5) and add the numerator (1). So, 8 1/5 = 41/5.
Now, let's compare the results:
- Option 1: 1 / 8^5
- Option 2: 8^5 = 32768
- Option 3: 1 / 5^8
- Option 4: 41/5
To determine which option is equivalent to 185, we need to find the option that equals 185.
Comparing the results, we can see that none of the options equals 185. Therefore, there is no correct option among the given choices that is equivalent to 185.