George Washington was an officer in the British army during the French and Indian War. He later used what he learned to lead the Revolutionary army.
Give one example of what Washington learned about different styles or methods of fighting that would help him lead the Americans to victory against the British in the Revolutionary War.
(2 points)
One example of what Washington learned about different styles or methods of fighting that would help him lead the Americans to victory against the British in the Revolutionary War was the importance of guerrilla warfare. During the French and Indian War, Washington observed Native American warriors and frontier settlers using guerrilla tactics effectively against the British forces. These tactics involved ambushing enemy forces, using natural cover to their advantage, and quickly retreating after an attack. Washington incorporated these strategies into the American Revolutionary army's warfare, allowing them to effectively target and weaken the larger and more traditional British forces.
Expand the properties of exponents to involve monomial bases with integer exponents to simplify the expression −25x85x
.(1 point)
Responses
−5x^7
negative 5 x superscript 7 baseline
−5x^8
negative 5 x superscript 8 baseline
−5x^9
negative 5 x superscript 9 baseline
5x^7
None of the provided responses are correct.
To simplify the expression −25x^8⋅5x^7, you need to multiply the coefficients and add the exponents with the same base.
When multiplying the coefficients, -25 and 5, you get -125.
When multiplying the variables with the same base, x^8 and x^7, you add the exponents, which gives you x^(8+7) = x^15.
Therefore, the simplified expression is -125x^15.
Expand the properties of exponents to involve monomial bases with integer exponents to simplify the expression −25x^8/5x
.(1 point)
Responses
−5x^7
negative 5 x superscript 7 baseline
−5x^8
negative 5 x superscript 8 baseline
−5x^9
negative 5 x superscript 9 baseline
5x^7
To simplify the expression −25x^8/5x, we can divide the coefficients and subtract the exponents with the same base.
When dividing the coefficients, -25 and 5, we get -5.
When subtracting the exponents with the same base, x^8 and x^1, we have (x^8)/(x^1) = x^(8-1) = x^7.
Therefore, the simplified expression is -5x^7.
Use the properties of integer exponents to simplify the expression (−4a^4)(−2a^2)
.(1 point)
Responses
8a^8
8 a superscript 8 baseline
8a^2
8 a superscript 2 baseline
−8a^6
negative 8 a superscript 6 baseline
8a^6
8 a superscript 6 baseline
To simplify the expression (−4a^4)(−2a^2), we can multiply the coefficients and add the exponents with the same base.
When multiplying the coefficients, -4 and -2, we get 8.
When multiplying the variables with the same base, a^4 and a^2, we add the exponents, which gives us a^(4+2) = a^6.
Therefore, the simplified expression is 8a^6.
Apply the properties of integer exponents to generate an equivalent algebraic expression to 3x^3y^−4/12x^7y^4
.(1 point)
Responses
1/4x^4y^8
Start Fraction 1 over 4 x superscript 4 baseline y superscript 8 baseline
4x^4y^8
4 x superscript 4 baseline y superscript 8 baseline
1/4x^12
Start Fraction 1 over 4 x superscript 12 baseline
3/12x^4y^8
To generate an equivalent algebraic expression for 3x^3y^−4/12x^7y^4, we can simplify the expression by applying the properties of integer exponents.
When simplifying the coefficients, 3 and 12, we can divide them both by their greatest common divisor, which is 3. Dividing 3 by 3 gives us 1, and dividing 12 by 3 gives us 4.
When dividing the variables with the same base, x^3 and x^7, we subtract the exponents, which gives us x^(7-3) = x^4.
Similarly, when dividing the variables with the same base, y^(-4) and y^4, we subtract the exponents, which gives us y^(-4+4) = y^0 = 1.
Therefore, the simplified expression is (1/4)x^4.
chose a answer choice
Apologies for any confusions. Based on the provided answer choices, the correct equivalent algebraic expression for 3x^3y^−4/12x^7y^4 is 1/4x^4y^8.
Apply the properties of integer exponents to simplify the algebraic expression (2xy3)4⋅(x2y)3
.(1 point)
Responses
32x^10y^11
32 x superscript 10 baseline y superscript 11 baseline
16x^25
16 x superscript 25 baseline
16x^10y^15
16 x superscript 10 baseline y superscript 15 baseline
x^10y^15
To simplify the algebraic expression (2xy^3)^4⋅(x^2y)^3, we need to apply the properties of integer exponents.
First, we can simplify the expression inside each set of parentheses:
(2xy^3)^4 equals (2^4)(x^4)(y^3)^4, which simplifies to 16x^4y^(3*4) = 16x^4y^12.
(x^2y)^3 equals (x^2)^3(y)^3, which simplifies to x^(2*3)y^3 = x^6y^3.
Now we can multiply the two simplified terms:
(16x^4y^12) * (x^6y^3) equals 16x^4x^6 * y^12y^3 = 16x^(4+6) * y^(12+3) = 16x^10 * y^15.
Therefore, the simplified expression is 16x^10y^15.
Apply the properties of integer exponents to simplify the algebraic expression (−5a3b4c−23a−4b0c3)−2
.(1 point)
Responses
925a12
Start Fraction 9 over 25 a superscript 12 baseline End Fraction
−5c103a14b8
Start Fraction negative 5 c superscript 10 baseline over 3 a superscript 14 baseline b superscript 8 baseline End Fraction
9c1025a14b8
Start Fraction 9 c superscript 10 baseline over 25 a superscript 14 baseline b superscript 8 baseline End Fraction
c10a14b8
Start Fraction c superscript 10 baseline over a superscript 14 baseline b superscript 8 baseline End Fraction
To simplify the algebraic expression (−5a^3b^4c^−2/3a^−4b^0c^3)^−2, we need to apply the properties of integer exponents.
First, let's simplify the expression inside the parentheses:
(−5a^3b^4c^−2)/(3a^−4b^0c^3) can be rewritten as (-5/3)(a^(3-(-4)))(b^(4-0))(c^(-2-3)), which simplifies to (-5/3)a^7b^4c^(-5).
To raise this expression to the power of -2, we invert the base and change the sign of the exponent:
((-5/3)a^7b^4c^(-5))^(-2) can be rewritten as 1/((-5/3)a^7b^4c^(-5))^2.
Squaring each term inside the expression, we have (1/((-5/3)a^7b^4c^(-5))^2 = 1/(25/9)(a^7)^2(b^4)^2(c^(-5))^2.
Simplifying further, we get 1/(25/9)a^14b^8c^(-10).
Dividing 1 by 25/9 is equivalent to multiplying by its reciprocal, so we have (9/25)a^14b^8c^(-10).
Therefore, the simplified expression is (9/25)a^14b^8c^(-10).