@BotGPT35, Apply the Properties of Integer Exponents to generate equivalent expressions to (4^3 ⋅ 7^−2)^−5/7^9 ⋅ 4^−13 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)
(4^3 ⋅ 7^−2)^−5/7^9 ⋅ 4^−13=
To generate equivalent expressions with positive exponents, we can use the rules of integer exponents.
First, let's simplify the expression inside the parentheses:
(4^3 ⋅ 7^−2)^−5
Using the rule (a^m)^n = a^(m*n), we can simplify:
= 4^(3 * -5) ⋅ 7^(-2 * -5)
= 4^(-15) ⋅ 7^10
Next, let's combine the expression outside the parentheses:
(4^(-15) ⋅ 7^10) / 7^9 ⋅ 4^(-13)
Using the rule a^m / a^n = a^(m-n):
= 4^(-15 - (-13)) ⋅ 7^(10 - 9)
= 4^(-15 + 13) ⋅ 7^1
= 4^(-2) ⋅ 7
Now, let's simplify the expression:
= 1/4^2 ⋅ 7
= 1/16 ⋅ 7
= 7/16
Therefore, the simplified fraction with no remaining exponents is 7/16.
To generate equivalent expressions with positive exponents, we can use the rules of integer exponents.
First, let's simplify the expression inside the parentheses:
(4^3 ⋅ 7^−2)^−5
Using the rule (a^m)^n = a^(m*n), we can simplify:
= 4^(3 * -5) ⋅ 7^(-2 * -5)
= 4^(-15) ⋅ 7^10
Next, let's combine the expression outside the parentheses:
(4^(-15) ⋅ 7^10) / 7^9 ⋅ 4^(-13)
Using the rule a^m / a^n = a^(m-n):
= 4^(-15 - (-13)) ⋅ 7^(10 - 9)
= 4^(-15 + 13) ⋅ 7^1
= 4^(-2) ⋅ 7
Finally, let's simplify the expression:
= 1/4^2 ⋅ 7
= 1/16 ⋅ 7
= 7/16
Therefore, the simplified fraction with no remaining exponents is 7/16.
What was one strength of the Articles of Confederation?
(1 point)
A. It allowed states to make decisions for themselves.
B. It gave the federal government power to impose taxes.
C. It gave Congress the authority to overturn decisions made by the president.
D. It provided Congress with a means to regulate trade.
A. It allowed states to make decisions for themselves.
Shays's rebellion in 1787 was in response to what? Select all that apply.
(1 point)
A. expansion of territories
B. the Northwest Ordinance
C. seizure of farms
D. increased taxes
C. seizure of farms
D. increased taxes
Which of the following was one of the principal authors of the Federalist Papers?
(1 point)
A. George Washington
B. Alexander Hamilton
C. Thomas Jefferson
D. John Adams
B. Alexander Hamilton
Which of the following was one of the principal authors of the Federalist Papers? (1 point)
A. George Washington
B. Alexander Hamilton
C. Thomas Jefferson
D. John Adams