Expand the properties of exponents to involve monomial bases with integer exponents to simplify the expression −25x^8/5x.(1 point)
Responses
−5x^9
negative 5 x superscript 9 baseline
5x^7
5 x superscript 7 baseline
−5x^7
negative 5 x superscript 7 baseline
−5x^8
negative 5 x superscript 8 baseline
Use the properties of integer exponents to simplify the expression (−4a^4)(−2a^2).(1 point)
Responses
8a^6
8 a superscript 6 baseline
8a^8
8 a superscript 8 baseline
−8a^6
negative 8 a superscript 6 baseline
8a^2
8 a superscript 6 baseline
To simplify the expression −25x^8/5x, we can apply the properties of exponents involving monomial bases with integer exponents.
First, let's simplify the coefficient -25/5, which gives us -5.
Next, for the variable part, x^8/ x, we can subtract the exponents since we have the same base (x). Therefore, x^8/x is equal to x^(8-1), which simplifies to x^7.
Finally, combining the coefficient and the variable, we get -5x^7 as the simplified expression.
To simplify the expression −25x^8/5x, we can apply the properties of exponents.
The first property states that when dividing two monomials with the same base, we subtract the exponents. In this case, we have x^8/5x, which can be rewritten as x^(8-1).
So, we now have -25x^7/5.
The second property states that when multiplying a monomial with a power to another monomial with the same base, we add the exponents. Here, we have -25x^7/5, which can be simplified as -25 * x^7/5.
Finally, we can simplify -25 * x^7/5 by multiplying the coefficients and keeping the base x^7 intact.
Thus, the simplified expression is -5x^7.