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simplify: 1. a^2b^-3 2. (5/3)^-3 3. (a^2b^0c)^0 4. x^-2y^3 5. 3x^-2 6. n^2/n^-3 please help!!

  • math -

    for (1),
    a^2 * b^(-3)
    note that when a term is raised to a negative exponent, we get its reciprocal and raise it by the positive exponent,, for example,
    2^(-4) = 1/(2^4) ; thus we can rewrite
    b^(-3) = 1/(b^3)
    therefore,
    a^2 * (1/(b^3))
    a^2 / b^3

    for (2),
    (5/3)^-3
    we do the same thing,, get the reciprocal, make the exponent positive and simplify:
    (3/5)^3
    27 / 125

    for (3),
    (a^2b^0c)^0
    note that any number (except zero) raised to zero is equal to 1,, thus assuming a, b and c are not equal to 0,
    (a^2b^0c)^0 = 1

    for (4),
    do you mean x^(-2) * y^(3) ? if so,
    it's the same as #1:
    (1/(x^2)) * y^3
    y^3 / x^2

    for (5),
    3x^-2
    it's also the same procedure as #1:
    3*(1 / (x^2))
    3/(x^2)

    for (6),
    (n^2) / (n^(-3))
    same procedure as #1,,
    (n^2) / (1/(n^3))
    simplifying,
    (n^2)*(n^3)
    note that when multiplying terms raised to exponents but have the same base, we can just add the exponents,, for example
    2^3 * 2^5 = 2^(3+5) = 2^8
    note that the base here is 2.
    therefore,
    (n^2)*(n^3) = n^(2+3) = n^5

    hope this helps~ :)

  • math -

    thanks! i really appreciate this :)

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