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22 January, 08:57

Simplify. Assume that all variables represent positive real numbers. sqrt[45][x]^[7][y]^[8]

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Answers (2)
  1. 22 January, 09:14
    0
    3 x^3 * y^4*√ (5x)

    Step-by-step explanation:

    Factor

    45: 3 * 3 * 5

    y^8 = y * y * y * y * y * y * y * y

    x^7 = x * x * x * x * x * x * x

    Now underline every pair.

    Rule: for every pair, take 1 outside the square root sign and throw the other one away. If any of the bases are left over, leave them under the square root sign.

    3 * y * y * y * y * x * x * x * √ (5 * y)

    Answer: 3 x^3 * y^4*√ (5x)
  2. 22 January, 09:52
    0
    3 x^3 y^4 sqrt (5x)

    Step-by-step explanation:

    sqrt (45x^7y^8)

    We know that sqrt (ab) = sqrt (a) sqrt (b)

    sqrt (45) sqrt (x^7) sqrt (y^8)

    sqrt (9*5) sqrt (x^2 * x^2 * x^2 * x) sqrt (y^2 * y^2 * y^2 * y^2)

    We know that sqrt (ab) = sqrt (a) sqrt (b)

    sqrt (9) sqrt (5) sqrt (x^2) sqrt (x^2) sqrt (x^2) sqrt (x) sqrt (y^2) sqrt (y^2) sqrt (y^2) sqrt (y^2)

    3 sqrt (5) x*x*x sqrt (x) y*y*y*y

    3 x^3 y^4 sqrt (5) sqrt (x)

    3 x^3 y^4 sqrt (5x)
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