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Evaluate the following expressions, showing each step:

Mathematics

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Answers

6 parts
a
2000
b
392
c
225
d
90000
e
768
f
-32000000

Step-by-step solution

16 steps

Here are the numerical values for each expression:

Part a· 2 steps

  1. Calculate the power of 10.

    103=10×10×10=100010^3 = 10 \times 10 \times 10 = 1000

  2. Multiply the result by 2.

    2×1000=20002 \times 1000 = 2000

    The numerical value is 2000\boxed{2000}.

Part b392

  1. Calculate 727^2.

    72=7×7=497^2 = 7 \times 7 = 49

  2. Calculate 232^3.

    23=2×2×2=82^3 = 2 \times 2 \times 2 = 8

  3. Multiply the results.

    49×8=39249 \times 8 = 392

    The numerical value is 392\boxed{392}.

Part c225

  1. Calculate (−3)2(-3)^2.

    (−3)2=(−3)×(−3)=9(-3)^2 = (-3) \times (-3) = 9

  2. Calculate (−5)2(-5)^2.

    (−5)2=(−5)×(−5)=25(-5)^2 = (-5) \times (-5) = 25

  3. Multiply the results.

    9×25=2259 \times 25 = 225

    The numerical value is 225\boxed{225}.

Part d90000

  1. Calculate 323^2.

    32=3×3=93^2 = 3 \times 3 = 9

  2. Calculate 10410^4.

    104=10×10×10×10=1000010^4 = 10 \times 10 \times 10 \times 10 = 10000

  3. Multiply the results.

    9×10000=900009 \times 10000 = 90000

    The numerical value is 90000\boxed{90000}.

Part e768

  1. Calculate 444^4.

    44=4×4×4×4=2564^4 = 4 \times 4 \times 4 \times 4 = 256

  2. Multiply the result by 3.

    3×256=7683 \times 256 = 768

    The numerical value is 768\boxed{768}.

Part f-32000000

  1. Calculate (−2)5(-2)^5.

    (−2)5=(−2)×(−2)×(−2)×(−2)×(−2)=−32(-2)^5 = (-2) \times (-2) \times (-2) \times (-2) \times (-2) = -32

  2. Calculate (−10)6(-10)^6.

    (−10)6=(−10)×(−10)×(−10)×(−10)×(−10)×(−10)=1000000(-10)^6 = (-10) \times (-10) \times (-10) \times (-10) \times (-10) \times (-10) = 1000000

  3. Multiply the results.

    −32×1000000=−32000000-32 \times 1000000 = -32000000

    The numerical value is −32000000\boxed{-32000000}.

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