Question 498211
The problem to solve is: 
(2b^4c^4)^2 x (4b^-3a^6)^-6 


Multiply the exponent of c by 4giving 

The answer is 

c^4 evaluates to  


Multiply the exponent of b by 4giving 

The answer is 

b^4 evaluates to  

Multiply and 2 

Multiply and 1 


The just gets copied along. 

The answer is 

 

2*b^4 evaluates to  

Multiply and 

Multiply the and 

Multiply and 


The just gets copied along. 

The just gets copied along. 

The answer is 

 

2*b^4*c^4 evaluates to  

Raising to the exponent 2 is the same as multiplying by itself 2 times. 

Multiply by 

Multiply and 

Multiply the and 

Multiply and 


Combine the and by adding the exponents, and keeping the c, to get 

Combine the and by adding the exponents, and keeping the b, to get 

The answer is 

 

 × = 

 

(2*b^4*c^4)^2*x evaluates to  


Multiply the exponent of a by 6giving 

The answer is 

a^6 evaluates to  

The 1 becomes a 1/1
The exponent, -3, is negative, so we'll have to handle it a little bit differently here.
But for now, we'll treat it as it was positive, and handle it in the usual manner... that is, as if it were at +3.


Multiply the exponent of b by 3giving 

Now, because of the negative exponent, we take this result, and turn it upside-down.
That is, a number becomes 1/the number, or a fraction is literally flipped upside-down.
This effectively "flips" the entire result upside down, but that's exactly what negative exponents do!
In this case...


The 1 becomes a 1/1
b^3 becomes 1/b^3.
The answer is 

b^-3 evaluates to  

Multiply and 4 

Multiply and 1 


The just gets copied along. 

The answer is 

 

4*b^-3 evaluates to  

Multiply and 

Multiply the and 

Multiply and 


The just gets copied along. 

The just gets copied along. 

The answer is 

 

4*b^-3*a^6 evaluates to  

The 4096 becomes a 1/4096
The exponent, -6, is negative, so we'll have to handle it a little bit differently here.
But for now, we'll treat it as it was positive, and handle it in the usual manner... that is, as if it were at +6.


Multiply the exponent of by 6giving 

Multiply the exponent of by 6giving 

Now, because of the negative exponent, we take this result, and turn it upside-down.
That is, a number becomes 1/the number, or a fraction is literally flipped upside-down.
This effectively "flips" the entire result upside down, but that's exactly what negative exponents do!
In this case...


The 1 becomes a 1/1
a^36 becomes 1/a^36.
b^-18 becomes 1/b^-18.
The answer is 

(4*b^-3*a^6)^-6 evaluates to  

Multiply and 

Multiply the and 

Multiply and 


Combine the and by adding the exponents, and keeping the b, to get 

The just gets copied along. 

The just gets copied along. 

The answer is 

 

(2*b^4*c^4)^2*x*(4*b^-3*a^6)^-6 evaluates to  



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The final answer is   
i/1024 b 26 c8a -36
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