Evaluate each expression for

Question

p = - 4

,

q equals 8

, and

r = - 10

.

\frac{3p + 3(4 + p)^3}{r + 8}

Accepted Answer

Hello Today we're going to be simplifying the indicated expression using the given values. So what we are given is negative M plus seven raised to the third power minus five N. All divided by seven minus O. And we are told that M is equal to negative nine N. Is equal to positive one and O is equal to negative 14. So we're going to be taking these values and substituting them N for M N. And O. In the given expression in order to simplify it. So let's go ahead and substitute in the values. If we substitute in the values we get negative M plus seven which is going to be negative nine plus seven raised to the third power minus five times N. Which is going to be five times one. All over seven minus O which is going to be seven minus negative 14. Now there's a bit of simplification that we can go ahead and do here five times one is going to give us five and negative nine plus seven is going to give us negative two And finally negative one times negative 14 is going to give us positive 14. So if we simplify these values, what we get is negative negative to race to the third. Power minus five. All over seven plus 14 to simplify the denominator seven plus 14 is going to give us 21. So we have negative negative two to the third minus five over positive 21. Now in order to simplify the numerator let's go ahead and evaluate negative two to the third Power negative two to the third. Power is the same thing as saying negative two multiplied by itself three different times and negative two times two is going to give us positive four and positive four times negative two is going to give us negative eight. So negative two to the third Power evaluates to negative eight. But keep in mind that this negative number sits outside the parentheses. So once we substituting this value, the numerator now becomes negative negative -5 over positive 21 and negative one times negative eight is going to give us positive eight for the numerator and positive eight minus five is going to give us three. So this simplifies to 3/21. Now there's one more simplification simplification that we can do the numerator three and the denominator 21 are both divisible by three. So if we divide both the numerator and denominator by three, this is going to give us the fraction 1/7 and this is going to be the simplified version of the original expression and with that being said, the answer to this problem is going to be d So I hope this video helps you in understanding how to approach this problem and I'll go ahead and see you all in the next video

Evaluate each expression for $p = - 4$ , $q equals 8$ , and $r = - 10$ . $\frac{3p + 3(4 + p)^3}{r + 8}$

Key Concepts

Order of Operations

Substitution of Variables

Exponentiation

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