Expand the properties of exponents to involve monomial bases with integer exponents to simplify the expression −25x^8/5x.(1 point)
Responses
5x^7
5 x superscript 7 baseline
−5x^9
negative 5 x superscript 9 baseline
−5x^8
negative 5 x superscript 8 baseline
−5x^7
negative 5 x superscript 7 baseline
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^6
negative 8 a superscript 6 baseline
8a^2
8 a superscript 2 baseline
8a^6
8 a superscript 6 baseline
8a^6
Apply the properties of integer exponents to generate an equivalent algebraic expression to 3x^3y^−4/12x^7y^4.(1 point)
Responses
3/12x^4y^8
Start Fraction 3 over 12 x superscript 4 baseline y superscript 8 baseline
1/4x^12
Start Fraction 1 over 4 x superscript 12 baseline
4x^4y^8
4 x superscript 4 baseline y superscript 8 baseline
1/4x^4y^8
Start Fraction 1 over 4 x superscript 4 baseline y superscript 8 baseline
To simplify the expression -25x^8/5x, we can apply the properties of exponents. When dividing monomials with the same base, we subtract the exponents:
-25x^8/5x = -25/5 * x^8/x
Simplifying the coefficient, -25/5 = -5.
Now, when we divide x^8 by x, we subtract the exponents, which gives us x^8-1 = x^7.
So, the simplified expression is -5x^7.
To simplify the expression −25x^8/5x, we can use the properties of exponents.
First, let's simplify the expression -25x^8 divided by 5x separately.
For −25x^8 divided by 5x, we can divide the coefficients and subtract the exponents.
-25 divided by 5 is -5.
In terms of the variables, x^8 divided by x is x^(8-1) = x^7.
Therefore, −25x^8/5x simplifies to -5x^7.
So, the correct answer is 5x^7.