Expert: Sherman D. - 4/24/2008

Question
QUESTION: Simplify the expression...

7x to the negative 8 power times 6x to the 3rd power.

(-10g to the 7th power) times 2h to the 9th power times 3g to the fifth power.

(9q to the 2nd power) and 3 on outside of parenthesis.

(3xy to the 3rd power) 2 (xy)6 on outside of parenthesis.

7 to the 10th power over
7 to the 8th power

5t over
3 in parenthesis, to the 3rd power.

ANSWER: 7x^-8 * 6x^3
(7 * 6) * x^(-8 + 3)
42x^-5

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I don't know if you left something out on this one or not.

-10g^7 * 2h^9 * 3g^5 = (-10 * 2 * 3) * g^(7 + 5) * h^9 = -60g^12h^9

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(9q^2)^3 = 9^3 * (q^2)^3 = 729q^(2 * 3) = 729q^6

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(3xy^3)^2 * (xy)^6 = 9x^2y^6 * x^6y^6 = 9x^8y^12

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(7^10)/(7^8) = 7^(10 - 8) = 7^2 = 49

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(5t/3)^3 = (125t^3)/27

---------- FOLLOW-UP ----------

QUESTION: Tell whether the system has no solution, 1 solution, or infinitely many solutions...

y=-2x-5
y=-2x+4

y=5x-2
y=-x+3

Solve the system using elimination...

2x+5y=-18
2x-5y=22

2x+y=0
5x+2y=2

Simplify the expression...

3 over c to the -4 power and d to the 3rd power

Answer
y=-2x-5
y=-2x+4

Same Slope but different y-intercepts

ANS : No Solution

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y=5x-2
y=-x+3

different slopes and different y-intercepts

ANS : 1 solution

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Solve the system using elimination...

2x+5y=-18
2x-5y=22

4x = 4
x = 1

2(1) + 5y = -18
2 + 5y = -18
5y = -20
y = -4

ANS : (1,-4)

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2x+y=0
5x+2y=2

Multiply top by -2

-4x - 2y = 0
5x + 2y = 2

x = 2

2(2) + y = 0
4 + y = 0
y = -4

ANS : (2,-4)

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Simplify the expression...

3 over c to the -4 power and d to the 3rd power

If by this you mean

(3/(c^-4d^3)) = (3c^4)/(d^3) or 3c^4d^-3