The primary goal of ________ is to maintain and enforce standards relating to the country’s environmental laws through extensive research, ecological assessments, and collaborative efforts with state, tribal, and local governments.
(1 point)
Responses
the Environmental Protection Agency
the Environmental Protection Agency
the Parks and Rec Service
the Parks and Rec Service
the Department of Labor
the Department of Labor
the Food and Drug Administration
15 answers
the Environmental Protection Agency
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Which of the following is an equivalent expression to 5 to the power of 9 ⋅ 5 to the power of −13 with only positive exponents that has been generated by applying the Properties of Integer Exponents?
a. 1/625
b. 5 to the power of 4
c. 5 to the power of 9/5 to the power of −13
d. 1/5 to the point of 4
a. 1/625
b. 5 to the power of 4
c. 5 to the power of 9/5 to the power of −13
d. 1/5 to the point of 4
To simplify the given expression and rewrite it with positive exponents, we can make use of the property of exponents that states:
a^m / a^n = a^(m-n)
So, 5^9 / 5^-13 can be rewritten as 5^(9 - (-13)) = 5^(9 + 13) = 5^22.
Therefore, the equivalent expression with only positive exponents is 5 to the power of 22.
Thus, the correct answer from the options provided would be:
b. 5 to the power of 4
a^m / a^n = a^(m-n)
So, 5^9 / 5^-13 can be rewritten as 5^(9 - (-13)) = 5^(9 + 13) = 5^22.
Therefore, the equivalent expression with only positive exponents is 5 to the power of 22.
Thus, the correct answer from the options provided would be:
b. 5 to the power of 4
Which property of exponents was used to generate the equivalent expression 3 to the power of 14 from 3 to the power of 5/3 to the power of −9?
A. only the Property of Negative Exponents
B. the Property of Negative Exponents and the Product Rule of Exponents
C. only the Product Rule of Exponents
D. only the Power Rule of Exponents
A. only the Property of Negative Exponents
B. the Property of Negative Exponents and the Product Rule of Exponents
C. only the Product Rule of Exponents
D. only the Power Rule of Exponents
To generate the equivalent expression 3 to the power of 14 from 3 to the power of 5/3 to the power of −9, we can use the property of exponents that states:
(a^m)^n = a^(m*n)
In this case, we have (3^(5/3))^(-9).
Using the property mentioned above, we can write this as 3^(5/3 * -9), which simplifies to 3^(-15).
Therefore, the correct answer is:
A. only the Property of Negative Exponents
(a^m)^n = a^(m*n)
In this case, we have (3^(5/3))^(-9).
Using the property mentioned above, we can write this as 3^(5/3 * -9), which simplifies to 3^(-15).
Therefore, the correct answer is:
A. only the Property of Negative Exponents
hmmm...can you explain more please? if that's not any trouble...
Certainly! Let's break it down step by step.
We start with the given expression: 3 to the power of 5/3 to the power of -9.
To simplify this expression, we can use the property of exponents that states:
(a^m)^n = a^(m*n)
In our case, a is 3, m is 5/3, and n is -9.
So, applying the property, we can rewrite the expression as follows: (3^(5/3))^(-9).
Next, we need to simplify the exponent of (3^(5/3))^(-9).
To do this, we multiply the exponents, which gives us 5/3 * -9.
Multiplying 5/3 by -9, we get -15.
So, the expression simplifies to (3^(-15)).
Therefore, the equivalent expression is 3 to the power of -15.
In summary, we used the property of exponents (a^m)^n = a^(m*n) to simplify the given expression step by step and arrived at 3 to the power of -15.
We start with the given expression: 3 to the power of 5/3 to the power of -9.
To simplify this expression, we can use the property of exponents that states:
(a^m)^n = a^(m*n)
In our case, a is 3, m is 5/3, and n is -9.
So, applying the property, we can rewrite the expression as follows: (3^(5/3))^(-9).
Next, we need to simplify the exponent of (3^(5/3))^(-9).
To do this, we multiply the exponents, which gives us 5/3 * -9.
Multiplying 5/3 by -9, we get -15.
So, the expression simplifies to (3^(-15)).
Therefore, the equivalent expression is 3 to the power of -15.
In summary, we used the property of exponents (a^m)^n = a^(m*n) to simplify the given expression step by step and arrived at 3 to the power of -15.
Which of the following is an equivalent expression to 15 to the power of 0 ⋅ 7 to the power of −2/(−4) to the power of −3 with only positive exponents that has been generated by applying the Properties of Integer Exponents?
a. 1/7 to the power of 2 ⋅ (−4) to the power of −3
b. 7 to the power of 2/(−4) to the power of 3
c. (−4) to the power of 3/ 7 to the power of 2
d. 4 to the power of 3/7 to the power of 2
a. 1/7 to the power of 2 ⋅ (−4) to the power of −3
b. 7 to the power of 2/(−4) to the power of 3
c. (−4) to the power of 3/ 7 to the power of 2
d. 4 to the power of 3/7 to the power of 2
To simplify the given expression and rewrite it with positive exponents, we can apply the properties of integer exponents.
First, remember that any non-zero number raised to the power of 0 is equal to 1. So, 15^0 can be simplified to 1.
Next, we can apply the property of negative exponents:
a^(-n) = 1 / (a^n)
Using this property, we can simplify 7^(-2/(−4))^(-3) to (7^(2/(-4)))^3 = 7^(-1/2)^3.
Finally, we can apply the property of exponentiation:
(a^m)^n = a^(m * n)
Using this property, we can simplify (7^(-1/2))^3 as 7^((-1/2) * 3) = 7^(-3/2).
Therefore, the equivalent expression with only positive exponents is 7^(3/2).
Thus, the correct answer from the options provided would be:
c. (−4) to the power of 3/ 7 to the power of 2
First, remember that any non-zero number raised to the power of 0 is equal to 1. So, 15^0 can be simplified to 1.
Next, we can apply the property of negative exponents:
a^(-n) = 1 / (a^n)
Using this property, we can simplify 7^(-2/(−4))^(-3) to (7^(2/(-4)))^3 = 7^(-1/2)^3.
Finally, we can apply the property of exponentiation:
(a^m)^n = a^(m * n)
Using this property, we can simplify (7^(-1/2))^3 as 7^((-1/2) * 3) = 7^(-3/2).
Therefore, the equivalent expression with only positive exponents is 7^(3/2).
Thus, the correct answer from the options provided would be:
c. (−4) to the power of 3/ 7 to the power of 2
Which of the following is the equivalent expression to (15 to the power of −3 ⋅ 4 to the power of 7) to the power of 0/4 to the power of −3 that has been generated by applying the Properties of Integer Exponents?
a. 64
b. 1⋅4 to the power of −3
c. 60/4 to the power of −3
d. 1/64
a. 64
b. 1⋅4 to the power of −3
c. 60/4 to the power of −3
d. 1/64
To simplify the given expression and rewrite it with positive exponents, we can apply the properties of integer exponents.
First, we have to understand that any non-zero number raised to the power of 0 is equal to 1. So, (15^(-3) * 4^7)^0 can be simplified to 1^0.
Using the property of a number raised to the power of 0 as 1, the expression becomes 1.
Therefore, the equivalent expression with only positive exponents is 1.
Hence, the correct answer from the options provided would be:
d. 1/64
First, we have to understand that any non-zero number raised to the power of 0 is equal to 1. So, (15^(-3) * 4^7)^0 can be simplified to 1^0.
Using the property of a number raised to the power of 0 as 1, the expression becomes 1.
Therefore, the equivalent expression with only positive exponents is 1.
Hence, the correct answer from the options provided would be:
d. 1/64
Which of the following is an equivalent expression to (2−3 ⋅93)−429 ⋅9−10 with only positive exponents, generated by applying the Properties of Integer Exponents?(1 point)
Responses
23 ⋅92
2 cubed times 9 squared
212⋅9−1229⋅9−10
Start fraction 2 superscript 12 baseline times 9 superscript negative 12 baseline over 2 superscript 9 baseline times 9 superscript negative 10 baseline end fraction
2392
Start Fraction 2 cubed over 9 squared end fraction
2−7⋅9−129⋅9−10
Responses
23 ⋅92
2 cubed times 9 squared
212⋅9−1229⋅9−10
Start fraction 2 superscript 12 baseline times 9 superscript negative 12 baseline over 2 superscript 9 baseline times 9 superscript negative 10 baseline end fraction
2392
Start Fraction 2 cubed over 9 squared end fraction
2−7⋅9−129⋅9−10
To simplify the given expression and rewrite it with positive exponents, we can apply the properties of integer exponents.
Let's break it down step by step:
First, we deal with the exponent expression 2^(-3) * 9^3.
Applying the property of negative exponents, we know that a^(-n) = 1 / (a^n). So, 2^(-3) can be rewritten as 1 / 2^3 = 1 / 8.
Similarly, 9^3 can be simplified to 729.
Next, we have to evaluate the term (1 / 8) - 429 * 9^(-12) * 9^(-10).
Since 9^(-12) * 9^(-10) can be simplified as 1 / (9^12 * 9^10) = 1 / 9^22, the expression becomes (1 / 8) - 429 * (1 / 9^22).
Further simplifying, we have to evaluate the expression (1 / 8) - (429 / 9^22).
To subtract the fractions, we need a common denominator. The common denominator is 8 * 9^22.
So, the expression becomes (1 / 8) - (429 * 9^22) / (8 * 9^22).
Combining the terms over the common denominator, we get (1 - 429 * 9^22) / (8 * 9^22).
Thus, the equivalent expression with only positive exponents is:
212 * 9^-12 * 9^-10
Therefore, the correct answer from the options provided would be:
c. 212 * 9^-12 * 9^-10
Let's break it down step by step:
First, we deal with the exponent expression 2^(-3) * 9^3.
Applying the property of negative exponents, we know that a^(-n) = 1 / (a^n). So, 2^(-3) can be rewritten as 1 / 2^3 = 1 / 8.
Similarly, 9^3 can be simplified to 729.
Next, we have to evaluate the term (1 / 8) - 429 * 9^(-12) * 9^(-10).
Since 9^(-12) * 9^(-10) can be simplified as 1 / (9^12 * 9^10) = 1 / 9^22, the expression becomes (1 / 8) - 429 * (1 / 9^22).
Further simplifying, we have to evaluate the expression (1 / 8) - (429 / 9^22).
To subtract the fractions, we need a common denominator. The common denominator is 8 * 9^22.
So, the expression becomes (1 / 8) - (429 * 9^22) / (8 * 9^22).
Combining the terms over the common denominator, we get (1 - 429 * 9^22) / (8 * 9^22).
Thus, the equivalent expression with only positive exponents is:
212 * 9^-12 * 9^-10
Therefore, the correct answer from the options provided would be:
c. 212 * 9^-12 * 9^-10
1 answer