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Problem one: Divide and simplify d^7/d^13

2 a). solve 5x^2=15
b). find the x-intercepts of f(x)=5x^2-15

3. Simplify by taking roots of the numerator and the denominator. Assume that all expressions under radicals represent positive: 3sqrt216x^8/y^3

4.Multiply and simplify. Assume variables represent nonzero real numbers: y^15 y^0

5. Subtract and simplify by collecting like radical terms if possible if possible: 7sqrt32-7sqrt2

6.In a right triangle find the length of the side not given b=2, c=sqrt13 the length of the third side is ?

7. Use the foil method to find the product: (8x^3-9)(x^9-3)

#### Solution Preview

1. when dividing powers with the same base, just subtract the exponents, so d^7/d^13 = d^{7 - 13} = d^{-6}

2. this implies x^2 = 3, so x = sqrt(3) or x = -- sqrt(3); and these are the same as the intercepts of f(x) = 5x^2 - 15

3. I'll ...

#### Solution Summary

This provides an example of working with exponents, solving radical equations, solving quadratic equations, and FOIL.

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