Question

(6^-6*36^5)^-4/36^-12*6^3

Answer 1

Ответ: 1) 6^-6*36^5=6^(-6+2*5)=6^4

2) (6^4)^-4=6^-16

3) 36^-12*6^3=6^(-24+3)=6^-21

4) 6^-16/6^-21=6^(21-15)=6^5.

Ответ 6^5.

Пошаговое объяснение:

Answer 2

Let's simplify the expression step by step:

Step 1: Simplify the base inside the parenthesis first: (6^-6 * 36^5)

Step 2: Simplify the exponent outside the parenthesis: (6^-6 * 36^5)^-4

Step 3: Simplify the base inside the second part of the expression: 36^-12 * 6^3

Step 4: Divide the results from Step 2 and Step 3: (6^-6 * 36^5)^-4 / (36^-12 * 6^3)

Let's proceed with each step:

Step 1: Simplify the base inside the parenthesis first: 6^-6 = 1 / 6^6 36^5 = 36 * 36 * 36 * 36 * 36

Step 2: Simplify the exponent outside the parenthesis: (1 / 6^6 * 36 * 36 * 36 * 36 * 36)^-4

Step 3: Simplify the base inside the second part of the expression: 36^-12 = 1 / 36^12 6^3 = 6 * 6 * 6

Step 4: Divide the results from Step 2 and Step 3: (1 / 6^6 * 36 * 36 * 36 * 36 * 36)^-4 / (1 / 36^12 * 6 * 6 * 6)

Now, to simplify further, we can move the terms in the denominator up to the numerator by changing the sign of the exponent (since dividing by a fraction is equivalent to multiplying by its reciprocal):

(36^12 * 6 * 6 * 6) / (6^6 * 36 * 36 * 36 * 36 * 36)^4

Now, simplify the common bases:

(6^3 * 6^3 * 6^3) / (6^6 * 36^4)

Now, combine the like terms:

6^(3+3+3-6) / 36^4

Simplify the exponents:

6^3 / 36^4

Now, write 36 as 6^2:

6^3 / (6^2)^4

Apply the power of a power rule (a^(m*n) = a^(mn)):

6^3 / 6^(2*4)

Simplify the exponent:

6^3 / 6^8

Now, apply the quotient rule (a^m / a^n = a^(m-n)):

6^(3-8)

Simplify the exponent:

6^-5

Finally, write 6^-5 as a fraction:

1 / 6^5

So, the simplified expression is 1 / 7776.