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
the Environmental Protection Agency
hellooo
Hello! How can I assist you today?
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
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
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
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
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.
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