Answer :
Raising the following we get,
(-3a^ (2)b^ (2)) ^ (2) is: 9a^ (4)b^ (4)
(3x^ (2)) ^ (3) is: 27x^ (6)
(-4x^ (4)) ^ (3) is: -64x^ (12)
(2x^ (2)y) ^ (4) is: 16x^ (8)y^ (4)
To raise each of the following expressions to the power of 21, we need to apply the exponent to each term within the parentheses. Here are the step-by-step solutions for each expression:
1. (-3a^(2)b^(2))^(2):
First, raise each term inside the parentheses to the power of 2:
(-3a^(2)b^(2))^(2) = (-3)^(2)(a^(2))^(2)(b^(2))^(2)
Next, simplify each term raised to the power of 2:
(-3)^(2) = 9
(a^(2))^(2) = a^(4)
(b^(2))^(2) = b^(4)
Finally, combine the simplified terms:
(-3a^(2)b^(2))^(2) = 9a^(4)b^(4)
2. (3x^(2))^(3):
First, raise the term inside the parentheses to the power of 3:
(3x^(2))^(3) = (3^(3))(x^(2)^(3))
Next, simplify the term raised to the power of 3:
3^(3) = 27
(x^(2)^(3)) = x^(6)
Finally, combine the simplified terms:
(3x^(2))^(3) = 27x^(6)
3. (-4x^(4))^(3):
First, raise the term inside the parentheses to the power of 3:
(-4x^(4))^(3) = (-4)^(3)(x^(4)^(3))
Next, simplify the term raised to the power of 3:
(-4)^(3) = -64
(x^(4)^(3)) = x^(12)
Finally, combine the simplified terms:
(-4x^(4))^(3) = -64x^(12)
4. (2x^(2)y)^(4):
First, raise the term inside the parentheses to the power of 4:
(2x^(2)y)^(4) = (2^(4))(x^(2)^(4))(y^(4))
Next, simplify each term raised to the power of 4:
2^(4) = 16
(x^(2)^(4)) = x^(8)
(y^(4)) = y^(4)
Finally, combine the simplified terms:
(2x^(2)y)^(4) = 16x^(8)y^(4)
So, the expressions raised to the power of 21 are as follows:
1. (-3a^ (2)b^ (2)) ^ (2) = 9a^ (4)b^ (4)
2. (3x^ (2)) ^ (3) = 27x^ (6)
3. (-4x^ (4)) ^ (3) = -64x ^ (12)
4. (2x^ (2)y) ^ (4) = 16x^ (8)y^ (4)
Learn more about functions:
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