Question

Please help!! This is so confusing! 100 points!!

Answer 1

`\Huge \boxed{\mathrm{4}}`

`\rule[225]{225}{2}`

Explanation:

`\displaystyle \sf (3^8 * 2^(-5) * 9^0)^(-2) * ((2^(-2))/(3^3 ) )^4 *3^(38)`

Distributing the power of -2 to the parenthesis,

`\displaystyle \sf (3^(-16) * 2^(10) * 9^0)* ((2^(-2))/(3^3 ) )^4 *3^(38)`

Distributing the power of 4 to the fraction,

`\displaystyle \sf (3^(-16) * 2^(10) * 9^0)* ((2^(-8))/(3^(12) ) )*3^(38)`

Multiplying,

`\displaystyle \sf (3^(-16) * 2^(10) * 9^0* 2^(-8) *3^(38))/(3^(12) )`

Simplifying,

`\displaystyle \sf (2^2 *3^(22))/(3^(22) )`

`\sf 2^2 =4`

`\rule[225]{225}{2}`

Answer 2

The value of the expression given is:

• 4

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.