Question 498211: Simplify
(2b^4c^4)^2 x (4b^-3a^6)^-6
Answer by dianne55(1)   (Show Source):
You can put this solution on YOUR website! 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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