we came up with an answer of 23, however the answer book says 25 -

3 times -2 squared times 10 plus 5 = -115

-7 to the 0 power is -1 times 5 = -5

-115/-5= 23

we came up with an answer of 23, however the answer book says 25 -

3 times -2 squared times 10 plus 5 = -115

-7 to the 0 power is -1 times 5 = -5

-115/-5= 23

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You are trying to solve for the following: (ab^{2}c+5)/(x^{0}y)

when given the following: a= 3, b= -2, c= 10, x= -7, and y= 5

This is what you did:

(ab^{2}c+5)/(x^{0}y) = ((3*-2^{2}*10)+5)/(-7^{0}*5)

= ((3*-4*10)+5)/(-1*5)

= (-120+5)/(-5)

= -115/-5

= 23

You made 2 mistakes. The first is in the numerator, where you squared 2 and then you took its negative rather than squaring -2. Since b=-2, then b^{2}=(-2)^{2}=(-2)*(-2)=4. If the problem had been -b^{2}, then -b^{2}=-(-2)^{2}=-(-2)*(-2)=-(4)=-4. The second mistake is in the denominator, where you raised 7 to the zero power and then took its negative rather than raising -7 to the zero power. Since x=-7, then x^{0}=(-7)^{0}=1. This isn't the same as -7^{0}, which implies that you are only raising 7 to the zero power (i.e., -7^{0}=-(7)^{0}=-(1)=-1).

So,

(ab^{2}c+5)/(x^{0}y) = ((3*(-2)^{2}*10)+5)/((-7)^{0}*5)

= ((3*4*10)+5)/(1*5)

= (120+5)/(5)

= 125/5

= 25

Hi Dianne,

I get 25. I have spotted a few errors.

"3 times -2 squared times 10 plus 5 = -115"

This is:

3 • (-2)^{2 }• 10 + 5

= 3 • 4 • 10 + 5

= 12 • 10 + 5

= 120 + 5

= 125

For the divisor (denominator), you say "-7 to the 0 power is -1 times 5 = -5"

Keep in mind that the problem was originally x^{0}y with x = -7 and y = 5.

(-7)^{0} • 5

= 1 • 5

= 5

The zero exponent applied to the x so it applies to the whole -7. Any number raised to the zero power is 1 (except 0^{0}, which is undefined).

Putting it all together you have

125 ÷ 5

= 25

I hope that helps. Good luck.