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Evaluate the cube root, the exponent, and the square root.

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Answers

4 parts
a

18\text{18}

b

66\text{66}

c

96\text{96}

d

11\text{11}

Step-by-step solution

14 steps

here are the calculations for the expressions:

Part a· 4 steps

Calculate 2163+42−16\sqrt[3]{216} + 4^2 - \sqrt{16}.

  1. Evaluate the cube root, the exponent, and the square root.

    2163=6\sqrt[3]{216} = 6 42=164^2 = 16 16=4\sqrt{16} = 4

  2. Substitute the values back into the expression.

    6+16−46 + 16 - 4

  3. Perform the addition.

    6+16=226 + 16 = 22

  4. Perform the subtraction.

    22−4=1822 - 4 = 18

    The simplified expression is:

    18\boxed{\text{18}}

Part b

66\text{66}

Calculate 92−273−1449^2 - \sqrt[3]{27} - \sqrt{144}.

  1. Evaluate the exponent, the cube root, and the square root.

    92=819^2 = 81 273=3\sqrt[3]{27} = 3 144=12\sqrt{144} = 12

  2. Substitute the values back into the expression.

    81−3−1281 - 3 - 12

  3. Perform the subtractions from left to right.

    81−3=7881 - 3 = 78 78−12=6678 - 12 = 66

    The simplified expression is:

    66\boxed{\text{66}}

Part c

96\text{96}

Calculate 33+43+253^3 + 4^3 + \sqrt{25}.

  1. Evaluate the exponents and the square root.

    33=273^3 = 27 43=644^3 = 64 25=5\sqrt{25} = 5

  2. Substitute the values back into the expression.

    27+64+527 + 64 + 5

  3. Perform the additions from left to right.

    27+64=9127 + 64 = 91 91+5=9691 + 5 = 96

    The simplified expression is:

    96\boxed{\text{96}}

Part d

11\text{11}

Calculate 144−23+49\sqrt{144} - 2^3 + \sqrt{49}.

  1. Evaluate the square roots and the exponent.

    144=12\sqrt{144} = 12 23=82^3 = 8 49=7\sqrt{49} = 7

  2. Substitute the values back into the expression.

    12−8+712 - 8 + 7

  3. Perform the subtraction.

    12−8=412 - 8 = 4

  4. Perform the addition.

    4+7=114 + 7 = 11

    The simplified expression is:

    11\boxed{\text{11}}
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