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

1 answer

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.