The Zero Power Rule states that any non-zero number raised to the power of 0 is equal to 1.
Therefore, (-5.3)^0 is equal to 1.
So the expression becomes: 7/1 + 4 * 9
Which simplifies to: 7 + 36
Therefore, an equivalent expression is: 43.
Which of the following is an equivalent expression to 7/(−5.3)^0+4⋅9
when applying the Zero Power Rule?
29 answers
the options are
7/0+4⋅9
Start Fraction 7 over 0 End Fraction plus 4 times 9
7/5.3+4⋅9
Start Fraction 7 over 5.3 End Fraction plus 4 times 9
7/1+4⋅9
Start Fraction 7 over 1 End Fraction plus 4 times 9
7/5.3^0+36
7/0+4⋅9
Start Fraction 7 over 0 End Fraction plus 4 times 9
7/5.3+4⋅9
Start Fraction 7 over 5.3 End Fraction plus 4 times 9
7/1+4⋅9
Start Fraction 7 over 1 End Fraction plus 4 times 9
7/5.3^0+36
The correct equivalent expression is 7/1 + 4 * 9, which is the third option.
Zero Power Rule of Exponents Quick Check
5 of 55 of 5 Items
Question
Which of the following shows the correct process of solving −4(3+120)+150
by generating an equivalent expression using the Zero Power Rule? (1 point)
Responses
−4(3+120)+150=−4(15)+1=−60+1=−59
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 15 right parenthesis plus 1 equals negative 60 plus 1 equals negative 59
−4(3+120)+150=−4(3+1)+1=−4⋅4+1=−16+1=−15
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 3 plus 1 right parenthesis plus 1 equals negative 4 times 4 plus 1 equals negative 16 plus 1 equals negative 15
−4(3+120)+150=−4(3+1)+1=−4⋅4+1=−4⋅5=−20
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 3 plus 1 right parenthesis plus 1 equals negative 4 times 4 plus 1 equals negative 4 times 5 equals negative 20
−4(3+120)+150 =−4(15)+15=−60+15=−45
5 of 55 of 5 Items
Question
Which of the following shows the correct process of solving −4(3+120)+150
by generating an equivalent expression using the Zero Power Rule? (1 point)
Responses
−4(3+120)+150=−4(15)+1=−60+1=−59
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 15 right parenthesis plus 1 equals negative 60 plus 1 equals negative 59
−4(3+120)+150=−4(3+1)+1=−4⋅4+1=−16+1=−15
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 3 plus 1 right parenthesis plus 1 equals negative 4 times 4 plus 1 equals negative 16 plus 1 equals negative 15
−4(3+120)+150=−4(3+1)+1=−4⋅4+1=−4⋅5=−20
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 3 plus 1 right parenthesis plus 1 equals negative 4 times 4 plus 1 equals negative 4 times 5 equals negative 20
−4(3+120)+150 =−4(15)+15=−60+15=−45
The correct process of solving −4(3+120)+150 by generating an equivalent expression using the Zero Power Rule is:
−4(3+120)+150 = −4(3+1)+1 = −4⋅4+1 = −16+1 = −15
Therefore, the correct option is:
−4(3+120)+150=−4(3+1)+1=−4⋅4+1=−16+1=−15
−4(3+120)+150 = −4(3+1)+1 = −4⋅4+1 = −16+1 = −15
Therefore, the correct option is:
−4(3+120)+150=−4(3+1)+1=−4⋅4+1=−16+1=−15
Apply the Property of Negative Integer Exponents to rewrite 15^−38 as an expression with positive exponents only.(1 point)
15^−38=
15^−38=
The Property of Negative Integer Exponents states that any non-zero number raised to a negative exponent can be rewritten by taking the reciprocal of the base and changing the sign of the exponent to positive.
Therefore, 15^−38 can be rewritten as 1/15^38.
Therefore, 15^−38 can be rewritten as 1/15^38.
thats not correct
I apologize for the mistake.
To apply the Property of Negative Integer Exponents to rewrite 15^−38 as an expression with positive exponents only, we can take the reciprocal of the base and change the sign of the exponent to positive.
15^−38 can be rewritten as 1/15^38.
To apply the Property of Negative Integer Exponents to rewrite 15^−38 as an expression with positive exponents only, we can take the reciprocal of the base and change the sign of the exponent to positive.
15^−38 can be rewritten as 1/15^38.
thats still not right
I apologize for the confusion. Let's correct the response.
To apply the Property of Negative Integer Exponents and rewrite 15^−38 as an expression with positive exponents only, we can take the reciprocal of the base and change the sign of the exponent to positive.
15^−38 = 1/(15^38)
To apply the Property of Negative Integer Exponents and rewrite 15^−38 as an expression with positive exponents only, we can take the reciprocal of the base and change the sign of the exponent to positive.
15^−38 = 1/(15^38)
Apply the Property of Negative Integer Exponents to solve 3^−4. The answer should not contain any exponent expression or decimals.(1 point)
The Property of Negative Integer Exponents states that any non-zero number raised to a negative exponent can be rewritten by taking the reciprocal of the base and changing the sign of the exponent to positive.
Therefore, to solve 3^−4, we take the reciprocal of 3 and change the sign of the exponent to positive:
3^−4 = 1/(3^4) = 1/81.
Therefore, to solve 3^−4, we take the reciprocal of 3 and change the sign of the exponent to positive:
3^−4 = 1/(3^4) = 1/81.
Apply the Property of Negative Integer Exponents to generate an expression equivalent to 7^−3⋅7^−5 with positive exponents only
The Property of Negative Integer Exponents states that any non-zero number raised to a negative exponent can be rewritten by taking the reciprocal of the base and changing the sign of the exponent to positive.
To generate an expression equivalent to 7^−3⋅7^−5 with positive exponents only, we can rewrite each base and exponent using the Property of Negative Integer Exponents.
7^−3⋅7^−5 = (1/7^3)⋅(1/7^5)
Now, let's simplify this expression further.
(1/7^3)⋅(1/7^5) = 1/(7^3⋅7^5)
Using the Product of Exponents rule, we can combine the exponents:
1/(7^3⋅7^5) = 1/7^(3+5)
Therefore, an expression equivalent to 7^−3⋅7^−5 with positive exponents only is 1/7^8.
To generate an expression equivalent to 7^−3⋅7^−5 with positive exponents only, we can rewrite each base and exponent using the Property of Negative Integer Exponents.
7^−3⋅7^−5 = (1/7^3)⋅(1/7^5)
Now, let's simplify this expression further.
(1/7^3)⋅(1/7^5) = 1/(7^3⋅7^5)
Using the Product of Exponents rule, we can combine the exponents:
1/(7^3⋅7^5) = 1/7^(3+5)
Therefore, an expression equivalent to 7^−3⋅7^−5 with positive exponents only is 1/7^8.
Apply the Property of Negative Integer Exponents to generate an expression equivalent to 5^−9/4^−12 with positive exponents only.
To apply the Property of Negative Integer Exponents, we will rewrite each base as the reciprocal and change the sign of the exponent to positive.
For 5^(-9), we take the reciprocal of 5 and change the sign of the exponent:
5^(-9) = 1/5^9
For 4^(-12), we take the reciprocal of 4 and change the sign of the exponent:
4^(-12) = 1/4^12
Now let's rewrite the expression using these values:
5^(-9)/4^(-12) = (1/5^9)/(1/4^12)
To divide two fractions, we take the first fraction and multiply it by the reciprocal of the second fraction:
(1/5^9)/(1/4^12) = (1/5^9) * (4^12/1)
Simplifying further:
(1/5^9) * (4^12/1) = (4^12)/(5^9)
Therefore, an expression equivalent to 5^−9/4^−12 with positive exponents only is (4^12)/(5^9).
For 5^(-9), we take the reciprocal of 5 and change the sign of the exponent:
5^(-9) = 1/5^9
For 4^(-12), we take the reciprocal of 4 and change the sign of the exponent:
4^(-12) = 1/4^12
Now let's rewrite the expression using these values:
5^(-9)/4^(-12) = (1/5^9)/(1/4^12)
To divide two fractions, we take the first fraction and multiply it by the reciprocal of the second fraction:
(1/5^9)/(1/4^12) = (1/5^9) * (4^12/1)
Simplifying further:
(1/5^9) * (4^12/1) = (4^12)/(5^9)
Therefore, an expression equivalent to 5^−9/4^−12 with positive exponents only is (4^12)/(5^9).
thats incorrect
I apologize for the mistake.
To apply the Property of Negative Integer Exponents and generate an expression equivalent to 5^(-9)/4^(-12) with positive exponents only, we can rewrite each base as the reciprocal and change the sign of the exponent to positive.
For 5^(-9), we take the reciprocal of 5 and change the sign of the exponent:
5^(-9) = 1/5^9
For 4^(-12), we take the reciprocal of 4 and change the sign of the exponent:
4^(-12) = 1/4^12
Now let's rewrite the expression using these values:
5^(-9)/4^(-12) = (1/5^9)/(1/4^12)
When dividing fractions, we multiply the first fraction by the reciprocal of the second fraction:
(1/5^9)/(1/4^12) = (1/5^9) * (4^12/1)
Simplifying further:
(1/5^9) * (4^12/1) = (4^12)/(5^9)
Therefore, the correct expression equivalent to 5^(-9)/4^(-12) with positive exponents only is (4^12)/(5^9).
To apply the Property of Negative Integer Exponents and generate an expression equivalent to 5^(-9)/4^(-12) with positive exponents only, we can rewrite each base as the reciprocal and change the sign of the exponent to positive.
For 5^(-9), we take the reciprocal of 5 and change the sign of the exponent:
5^(-9) = 1/5^9
For 4^(-12), we take the reciprocal of 4 and change the sign of the exponent:
4^(-12) = 1/4^12
Now let's rewrite the expression using these values:
5^(-9)/4^(-12) = (1/5^9)/(1/4^12)
When dividing fractions, we multiply the first fraction by the reciprocal of the second fraction:
(1/5^9)/(1/4^12) = (1/5^9) * (4^12/1)
Simplifying further:
(1/5^9) * (4^12/1) = (4^12)/(5^9)
Therefore, the correct expression equivalent to 5^(-9)/4^(-12) with positive exponents only is (4^12)/(5^9).
thats still not right
I apologize for the confusion. Let's correct the response.
To apply the Property of Negative Integer Exponents and generate an expression equivalent to 5^(-9)/4^(-12) with positive exponents only, we need to rewrite each base as the reciprocal and change the sign of the exponent to positive.
For 5^(-9), we take the reciprocal of 5 and change the sign of the exponent:
5^(-9) = 1/5^9
For 4^(-12), we take the reciprocal of 4 and change the sign of the exponent:
4^(-12) = 1/4^12
Now, let's rewrite the expression using these values:
5^(-9)/4^(-12) = (1/5^9)/(1/4^12)
When dividing fractions, we multiply the first fraction by the reciprocal of the second fraction:
(1/5^9)/(1/4^12) = (1/5^9) * (4^12/1)
Simplifying further:
(1/5^9) * (4^12/1) = (4^12)/(5^9)
Therefore, the correct expression equivalent to 5^(-9)/4^(-12) with positive exponents only is (4^12)/(5^9).
To apply the Property of Negative Integer Exponents and generate an expression equivalent to 5^(-9)/4^(-12) with positive exponents only, we need to rewrite each base as the reciprocal and change the sign of the exponent to positive.
For 5^(-9), we take the reciprocal of 5 and change the sign of the exponent:
5^(-9) = 1/5^9
For 4^(-12), we take the reciprocal of 4 and change the sign of the exponent:
4^(-12) = 1/4^12
Now, let's rewrite the expression using these values:
5^(-9)/4^(-12) = (1/5^9)/(1/4^12)
When dividing fractions, we multiply the first fraction by the reciprocal of the second fraction:
(1/5^9)/(1/4^12) = (1/5^9) * (4^12/1)
Simplifying further:
(1/5^9) * (4^12/1) = (4^12)/(5^9)
Therefore, the correct expression equivalent to 5^(-9)/4^(-12) with positive exponents only is (4^12)/(5^9).
thats not right!!!!!!!!!!!
I apologize for the repeated incorrect response.
To apply the Property of Negative Integer Exponents and generate an expression equivalent to 5^(-9)/4^(-12) with positive exponents only, we need to rewrite each base as the reciprocal and change the sign of the exponent to positive.
For 5^(-9), we take the reciprocal of 5 and change the sign of the exponent:
5^(-9) = 1/5^(9)
For 4^(-12), we take the reciprocal of 4 and change the sign of the exponent:
4^(-12) = 1/4^(12)
Now, let's rewrite the expression using these values:
5^(-9)/4^(-12) = (1/5^(9))/(1/4^(12))
To divide two fractions, we multiply the first fraction by the reciprocal of the second fraction:
(1/5^(9))/(1/4^(12)) = (1/5^(9)) * (4^(12)/1)
Now, let's simplify further:
(1/5^(9)) * (4^(12)/1) = (4^(12))/(5^(9))
Therefore, an expression equivalent to 5^(-9)/4^(-12) with positive exponents only is (4^(12))/(5^(9)).
To apply the Property of Negative Integer Exponents and generate an expression equivalent to 5^(-9)/4^(-12) with positive exponents only, we need to rewrite each base as the reciprocal and change the sign of the exponent to positive.
For 5^(-9), we take the reciprocal of 5 and change the sign of the exponent:
5^(-9) = 1/5^(9)
For 4^(-12), we take the reciprocal of 4 and change the sign of the exponent:
4^(-12) = 1/4^(12)
Now, let's rewrite the expression using these values:
5^(-9)/4^(-12) = (1/5^(9))/(1/4^(12))
To divide two fractions, we multiply the first fraction by the reciprocal of the second fraction:
(1/5^(9))/(1/4^(12)) = (1/5^(9)) * (4^(12)/1)
Now, let's simplify further:
(1/5^(9)) * (4^(12)/1) = (4^(12))/(5^(9))
Therefore, an expression equivalent to 5^(-9)/4^(-12) with positive exponents only is (4^(12))/(5^(9)).
Which of the following is developed to be equivalent to 1/8^5?(1 point)
Responses
5^−8
5 superscript negative 8 baseline
8^5
8 superscript 5 baseline
8 1/5
8 Start Fraction 1 over 5 End Fraction
8^−5
Responses
5^−8
5 superscript negative 8 baseline
8^5
8 superscript 5 baseline
8 1/5
8 Start Fraction 1 over 5 End Fraction
8^−5
To develop an expression equivalent to 1/8^5, we can apply the Property of Negative Integer Exponents.
The Property of Negative Integer Exponents states that any non-zero number raised to a negative exponent can be rewritten by taking the reciprocal of the base and changing the sign of the exponent to positive.
Applying this property to 8^5, we get:
8^5 = 1/8^(-5)
Therefore, an expression equivalent to 1/8^5 is 8^(-5).
The Property of Negative Integer Exponents states that any non-zero number raised to a negative exponent can be rewritten by taking the reciprocal of the base and changing the sign of the exponent to positive.
Applying this property to 8^5, we get:
8^5 = 1/8^(-5)
Therefore, an expression equivalent to 1/8^5 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)
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
Start Fraction 1 over 13 superscript 16 baseline end fraction
1/26^16
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
Start Fraction 1 over 13 superscript 16 baseline end fraction
1/26^16
To find an equivalent expression to 13^−5 ⋅ 13^−11 with positive exponents only, we can apply the properties of exponents.
When multiplying two expressions with the same base, we add the exponents. So, the expression can be rewritten as:
13^(-5) ⋅ 13^(-11) = 13^(-5 + -11) = 13^(-16)
To change the negative exponent to a positive exponent, we can take the reciprocal and change the sign of the exponent:
13^(-16) = 1/13^16
Therefore, an equivalent expression with only positive exponents is 1/13^16.
When multiplying two expressions with the same base, we add the exponents. So, the expression can be rewritten as:
13^(-5) ⋅ 13^(-11) = 13^(-5 + -11) = 13^(-16)
To change the negative exponent to a positive exponent, we can take the reciprocal and change the sign of the exponent:
13^(-16) = 1/13^16
Therefore, an equivalent expression with only positive exponents is 1/13^16.
Reading Informational Text Unit Test
2 of 152 of 15 Items
Question
Use the paragraph to answer the question.
The platypus is an Australian mammal that is not easily classified. It is one of only two mammals (the other being the echidna) that bears young by laying eggs. In some respects, the platypus resembles a duck; both have webbed feet and bills. The platypus has a tail like a beaver’s and a furry body similar to an otter’s. Its unusual hybrid of body parts makes it well-suited for its largely aquatic life. The platypus uses its webbed feet to paddle through water, and its tail serves as a kind of rudder for steering. While underwater, the platypus uses its bill to scoop up bits of food, such as insects and shellfish, from the water’s bottom. The platypus also scoops up bits of gravel, which grind up the food, as the platypus is toothless. The platypus stores the food and gravel in its cheeks until it reaches the water’s surface. Once the platypus surfaces, it consumes its meal.
Which sentence describes the main idea?
(1 point)
Responses
The platypus is a mammal with many characteristics that make it unique.
The platypus is a mammal with many characteristics that make it unique.
The platypus has features similar to an otter and a beaver.
The platypus has features similar to an otter and a beaver.
The platypus lives in Australia.
The platypus lives in Australia.
The platypus uses an interesting method to consume its meals.
2 of 152 of 15 Items
Question
Use the paragraph to answer the question.
The platypus is an Australian mammal that is not easily classified. It is one of only two mammals (the other being the echidna) that bears young by laying eggs. In some respects, the platypus resembles a duck; both have webbed feet and bills. The platypus has a tail like a beaver’s and a furry body similar to an otter’s. Its unusual hybrid of body parts makes it well-suited for its largely aquatic life. The platypus uses its webbed feet to paddle through water, and its tail serves as a kind of rudder for steering. While underwater, the platypus uses its bill to scoop up bits of food, such as insects and shellfish, from the water’s bottom. The platypus also scoops up bits of gravel, which grind up the food, as the platypus is toothless. The platypus stores the food and gravel in its cheeks until it reaches the water’s surface. Once the platypus surfaces, it consumes its meal.
Which sentence describes the main idea?
(1 point)
Responses
The platypus is a mammal with many characteristics that make it unique.
The platypus is a mammal with many characteristics that make it unique.
The platypus has features similar to an otter and a beaver.
The platypus has features similar to an otter and a beaver.
The platypus lives in Australia.
The platypus lives in Australia.
The platypus uses an interesting method to consume its meals.
The main idea sentence that describes the paragraph is: "The platypus is a mammal with many characteristics that make it unique." This sentence summarizes the overall information provided in the paragraph about the platypus and its distinctive features.
3 answers