Video Transcript
Simplify negative eight 𝑥 to the power of four multiplied by negative three 𝑥 to the power of five multiplied by negative 𝑥 to the power of four.
So the first thing we do when we deal with a problem like this is we deal with the coefficients before we deal with the 𝑥-terms. So we’ve got negative eight multiplied by negative three multiplied by negative one because, remember, if we’ve got negative 𝑥 to the power of four, it’s the same as negative one 𝑥 to the power of four. So when we’re multiplying our coefficients together, it’s worth remembering that if we’ve got a negative multiplied by a negative, this is equal to a positive. And if we’ve got a positive multiplied by a negative, this is equal to a negative.
So what we’re gonna do is carry out the calculation in two steps. So we’ve got negative eight multiplied by negative three, so this is gonna give us positive 24. And then we’ve got positive 24 multiplied by negative one. Well, a positive multiplied by a negative is a negative. So therefore, we’re gonna get negative 24. So this is gonna be our coefficient. Well then, next, what we’re gonna do is utilize one of our exponent rules. And this tells us that if we’ve got 𝑥 to the power of 𝑎 multiplied by 𝑥 to the power of 𝑏, it’s equal to 𝑥 to the power of 𝑎 plus 𝑏. So we add the exponents.
So we’re gonna have 𝑥 to the power of and then we’ve got four plus five plus four, which is gonna be 13. So therefore, we can say that if we simplify negative eight 𝑥 to the power of four multiplied by negative three 𝑥 to the power of five multiplied by negative 𝑥 to the power of four, this is equal to negative 24𝑥 to the power of 13.
