Expand the properties of exponents to involve monomial bases with integer exponents to simplify the expression −25x85x.(1 point)
Responses
−5x7
negative 5 x superscript 7 baseline
5x7
5 x superscript 7 baseline
−5x9
negative 5 x superscript 9 baseline
−5x8
The correct answer is 5x7.
To simplify the expression -25x^8 * 5x^5, we apply the properties of exponents with monomial bases and integer exponents.
The property states that when multiplying two monomials with the same base, we add their exponents. So, in this case, the base is x and the exponents are 8 and 5.
Applying the property, we add 8 and 5 to get a final exponent of 13. Therefore, the simplified expression is 5x^13.
However, none of the provided options matches this result. Therefore, none of the given responses is correct.
incorrect
Apologies for the incorrect response.
To simplify the expression -25x^8 * 5x^5, we again apply the properties of exponents with monomial bases and integer exponents.
The property for multiplying two monomials with the same base states that we add their exponents. So, in this case, the base is x and the exponents are 8 and 5.
Adding 8 and 5 gives us a final exponent of 13. Therefore, the simplified expression is -25x^13.
Use the properties of integer exponents to simplify the expression (−4a4)(−2a2).(1 point)
Responses
8a8
8 a superscript 8 baseline
8a6
8 a superscript 6 baseline
−8a6
negative 8 a superscript 6 baseline
8a2
To simplify the expression (-4a^4)(-2a^2), we can apply the properties of integer exponents.
When multiplying two monomials with the same base, we add their exponents. In this case, the base is "a" and the exponents are 4 and 2.
Adding 4 and 2 gives us a final exponent of 6. Therefore, the simplified expression is 8a^6.
So, the correct answer is: 8a^6.
Apply the properties of integer exponents to generate an equivalent algebraic expression to 3x3y−412x7y4.(1 point)
Responses
312x4y8
Start Fraction 3 over 12 x superscript 4 baseline y superscript 8 baseline
14x4y8
Start Fraction 1 over 4 x superscript 4 baseline y superscript 8 baseline
14x12
Start Fraction 1 over 4 x superscript 12 baseline
4x4y8
To generate an equivalent algebraic expression for 3x^3y-4/12x^7y^4, we can simplify the exponents and coefficients using the properties of integer exponents.
First, simplify the coefficient -4/12 by dividing both the numerator and denominator by their greatest common divisor (which is 4). This simplifies to -1/3.
Next, simplify the exponents.
For x, since we are subtracting exponents, we subtract 7 from 3. This gives us x^(3-7) = x^(-4).
For y, we are subtracting exponents again, so we subtract 4 from 1. This gives us y^(1-4) = y^(-3).
Putting it all together, the equivalent algebraic expression is:
-1/3x^(-4)y^(-3).
So, the correct answer is: Start Fraction negative 1 over 3 x superscript negative 4 baseline y superscript negative 3 baseline.
Apply the properties of integer exponents to simplify the algebraic expression (2xy3)4⋅(x2y)3.(1 point)
Responses
x10y15
x superscript 10 baseline y superscript 15 baseline
16x10y15
16 x superscript 10 baseline y superscript 15 baseline
32x10y11
32 x superscript 10 baseline y superscript 11 baseline
16x25
To simplify the algebraic expression (2xy^3)^4 * (x^2y)^3, we can apply the properties of integer exponents.
First, we simplify the expression inside the first parentheses:
(2xy^3)^4 = 2^4 * x^4 * (y^3)^4 = 16x^4 * y^12
Next, we simplify the expression inside the second parentheses:
(x^2y)^3 = (x^2)^3 * y^3 = x^6 * y^3
Now, we can multiply the two simplified expressions:
(16x^4 * y^12) * (x^6 * y^3) = 16x^4 * x^6 * y^12 * y^3 = 16x^(4+6) * y^(12+3) = 16x^10 * y^15
Therefore, the simplified expression is: 16x^10 * y^15.
Apply the properties of integer exponents to simplify the algebraic expression (−5a3b4c−23a−4b0c3)−2.(1 point)
Responses
c10a14b8
Start Fraction c superscript 10 baseline over 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
−5c103a14b8
Start Fraction negative 5 c superscript 10 baseline over 3 a superscript 14 baseline b superscript 8 baseline End Fraction
925a12