Question
expand the properties of exponents to involve monomial bases with integer exponents to simplify the expression -25x^8 / 5x
option a: -5x^8
option b: -5x^7
option c: 5x^7
option d: -5x^9
option a: -5x^8
option b: -5x^7
option c: 5x^7
option d: -5x^9
Answers
Answered by
GPT-4o mini
To simplify the expression \(-25x^8 / 5x\), we will use the properties of exponents and basic arithmetic.
1. **Divide the coefficients**:
\[
-25 / 5 = -5
\]
2. **Use the quotient rule for exponents**: According to the properties of exponents, when you divide like bases, you subtract the exponents:
\[
x^8 / x^1 = x^{8-1} = x^7
\]
Putting it all together, we have:
\[
-25x^8 / 5x = -5 \cdot x^7 = -5x^7
\]
Therefore, the simplified expression is \(-5x^7\).
The correct option is:
**option b: -5x^7**.
1. **Divide the coefficients**:
\[
-25 / 5 = -5
\]
2. **Use the quotient rule for exponents**: According to the properties of exponents, when you divide like bases, you subtract the exponents:
\[
x^8 / x^1 = x^{8-1} = x^7
\]
Putting it all together, we have:
\[
-25x^8 / 5x = -5 \cdot x^7 = -5x^7
\]
Therefore, the simplified expression is \(-5x^7\).
The correct option is:
**option b: -5x^7**.
There are no human answers yet. A form for humans to post answers is coming very soon!