Algebra 2

Exponential Notation

Evaluate the following:
x^3+y^-2 for x=-3 and y=4

I don't understand how to solve this equation. I solved it and got -11 as my answer but the books answer is -26 15/16

Thanks For Your Help

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  1. x^3 + y^(-2)
    to evaluate means you substitute the value of x and y which are given in the problem.
    first, recall some laws of exponents. if a term is raised by a negative number, it is also equal to its reciprocal raised to the that number but positive in sign. for example,
    5^(-3) = (1/5)^3
    thus we can actually rewrite this equation as
    x^3 + (1/y)^2
    substituting x = -3 and y = 4,
    (-3)^3 + (1/4)^2
    (-3)*(-3)*(-3) + (1/4)*(1/4)
    -27 + 1/16
    -26 15/16

    hope this helps~ :)

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  2. thanks so much :)) That was really helpful. Just one quick question. How did you get 15/16?

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  3. you can rewrite -27 as -26 16/16 (since 16/16 is just equal to 1). thus,
    -26 16/16 + 1/16
    -26 + (16-1)/16
    -26 15/16

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  4. ohh okk thanks so much :)

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