# Video: Evaluating Negative Single Term Mixed Number Expressions with Positive Integer Exponents

Which of the following is equal to (−2 1/4)³? [A] −8 1/64 [B] −11 25/64 [C] −6 3/4 [D] −2 3/12 [E] −27/12

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### Video Transcript

Which of the following is equal to negative two and one quarter to the third power? Option A) negative eight and one over 64, option B) negative 11 and 25 over 64, option C) negative six and three-quarters, option D) negative two and three-twelfths, option E) negative 27 over 12.

Let’s start this question by writing our fraction negative two and one-quarter as a top heavy or improper fraction. Let’s start by taking our fraction two and a quarter ignoring the negative for a second and visualising it as two whole shapes and one-quarter. If we split our two whole shapes into quarters, we would have four-quarters in each one plus our one-quarter leftover. So two and quarter is equivalent to nine over four. So negative two and a quarter is equivalent to negative nine over four. So finding the third power of negative two and a quarter is equal to finding the third power of negative nine over four.

We can recall that finding the third power of a value 𝑥 is equivalent to working out 𝑥 times 𝑥 times 𝑥. So for negative nine over four to the third power, we can work out negative nine over four times negative nine over four times negative nine over four. Note that since the negative was also part of the number taken to the third power, then it appears three times as well. This line is equivalent to negative nine times negative nine times negative nine over four times four times four, since when we multiply fractions, we can multiply the numerator is together and the denominators together. It’s important that we put the negatives only on the numerator or only on the denominator, but not both.

To start evaluating our numerator, we multiply a negative nine by negative nine, which is 81. Notice that we have a positive value here, since two negatives multiplied will always give a positive value. Next, we work out 81 times negative nine giving us negative 729. Next, we work out four times four on the denominator giving us 16. And then we multiply this by four which is 64. So our answer then is negative 729 over 64. And now we put answer into a mixed number form since that is the form given in the question and in the answer options. To do this, we need to work out how many times 64 goes into negative 729. Our calculation in this case would be negative 729 divided by 64 which we can do without a calculator using a long division method.

We can work out 729 divided by 64 and then restore the negative into our answer at the end. Using the division method, we can see that there is a whole number answer of 11 and a remainder of 25. So for our mixed number answer to negative 729 over 64, we can start by restoring our negative. The 11 is the whole number answer. The remainder of 25 will be the numerator of our fraction. And we put 64 as our denominator, since it’s the number we divided by and the number of powers in our fraction. So our answer then is the one given an option B, negative 11 and 25 over 64.