Expand the properties of exponents to involve monomial bases with integer exponents to simplify the expression −25x85x.(1 point)
Responses
−5x9
negative 5 x superscript 9 baseline
−5x8
negative 5 x superscript 8 baseline
5x7
5 x superscript 7 baseline
−5x7
negative 5 x superscript 7 baseline
To expand the properties of exponents for monomial bases with integer exponents, we use the rule:
a^m * a^n = a^(m + n)
In the given expression -25x^8 * 5x^7, we can apply this rule as follows:
-25x^8 * 5x^7 = -25 * 5 * x^8 * x^7
Simplifying, we get:
= -125 * x^(8 + 7)
= -125 * x^15
Therefore, the simplified expression is -125x^15.
Well, let's see if we can have some fun with this! To simplify the expression −25x^8, we just need to remember that when you multiply two numbers with the same base, you just have to add their exponents. So, in this case, we have -25 times x raised to the power of 8. And since there are no other terms to multiply by, we can't simplify further, except to express it as -25x^8. But don't worry, math doesn't always have to be so negative! Keep on crunching those numbers!
To simplify the expression −25x^8 * 5x^7, we can use the properties of exponents for monomial bases with integer exponents:
1. When multiplying two monomials with the same base, we add their exponents.
So, the exponents for x in the expression −25x^8 * 5x^7 will be added:
x^8 * x^7 = x^(8+7) = x^15
2. When multiplying two numbers with different signs, the result is negative.
Since −25 and 5 have different signs, the result will be negative:
−25 * 5 = −125
Putting it all together, we get:
−25x^8 * 5x^7 = −125x^15
To simplify the expression −25x^8 \cdot 5x^7, we can apply the properties of exponents. When multiplying monomials with the same base, we can add their exponents.
First, let's simplify the numerical coefficients: −25 \cdot 5 = -125.
Now, let's simplify the variable terms. The base is "x" and the exponents are 8 and 7. To multiply the variable terms, we again add the exponents: x^8 \cdot x^7 = x^(8+7) = x^15.
Putting it all together, the simplified expression is -125x^15.
So, the correct response is −125x^15.