Respuesta :

yersanabria

Answer:

The value of the expression given is:

  • 4

Step-by-step explanation:

First, you must divide the expression in three, and to the final, you can multiply it:

  1. [(3^8)*(2^(-5))*(9^0)]^(-2)
  2. [(2^(-2))/(3^3)]^4
  3. 3^28

Now, we can solve each part one by one:

First part.

  • 3^8 = 6561
  • 2^(-5) = 0.03125
  • 9^0 = 1 (Whatever number elevated to 0, its value is 1)
  • (6561 * 0,03125 * 1) = 205.03125

And we elevate this to -2:

  • 205.03125^-2 = 2.378810688*10^(-5) or 0.00002378810688

Second part.

  • 2^(-2) = 0.25
  • 3^3 = 27
  • 0.25 / 27 = 9.259259259 * 10^(-3) or 0.00925925925925

And we elevate this to 4:

  • 0.00925925925925^4 = 7.350298528 * 10^(-9) or 0.000000007350298528

Third Part.

  • 3^28 = 2.287679245 * 10^13 or 22876792450000

At last, we multiply all the results obtained:

  • 0.00002378810688 * 0.000000007350298528 * 22876792450000 = 3.999999999999999999 approximately 4

We approximate the value because the difference to 4 is minimal, which could be obtained if we use all the decimals in each result.

09pqr4sT

Answer:

[tex]\Huge \boxed{\mathrm{4}}[/tex]

[tex]\rule[225]{225}{2}[/tex]

Step-by-step explanation:

[tex]\displaystyle \sf (3^8 * 2^{-5} * 9^0)^{-2} * (\frac{2^{-2}}{3^3 } )^4 *3^{38}[/tex]

Distributing the power of -2 to the parenthesis,

[tex]\displaystyle \sf (3^{-16} * 2^{10} * 9^0)* (\frac{2^{-2}}{3^3 } )^4 *3^{38}[/tex]

Distributing the power of 4 to the fraction,

[tex]\displaystyle \sf (3^{-16} * 2^{10} * 9^0)* (\frac{2^{-8}}{3^{12} } )*3^{38}[/tex]

Multiplying,

[tex]\displaystyle \sf \frac{3^{-16} * 2^{10} * 9^0* 2^{-8} *3^{38}}{3^{12} }[/tex]

Simplifying,

[tex]\displaystyle \sf \frac{2^2 *3^{22}}{3^{22} }[/tex]

[tex]\sf 2^2 =4[/tex]

[tex]\rule[225]{225}{2}[/tex]

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