#1
What is the simplified form of √(16x^6)
4x^3
ExplanationThe square root of 16 is 4, and half the exponent of x^6 is 3.
#2
What is (27x^4)^(1/3) equivalent to?
3x
ExplanationCube root of 27 is 3, and the exponent simplifies to x.
#3
What is the simplified form of √(9x^2) + √(16x^4)?
7x^3
ExplanationSquare roots combine as 3x + 4x = 7x.
#4
What is the value of (64x^6)^(1/6)?
4x
ExplanationThe sixth root cancels the exponent, leaving 4x.
#5
What is the simplified form of (√(4x^5) * √(25x^3)) / (2x^2)?
5x^(5/2)
ExplanationSimplify square roots and divide.
#6
What is the value of (125x^6)^(-1/3)?
5x
ExplanationCube root of 125 is 5, and exponent becomes -2.
#7
What is the value of √(25x^8) / √(5x^2)?
5x^4
ExplanationSquare root of 25 is 5, and subtracting exponents gives x^(8-2) = x^6.
#8
What is the simplified form of (8x^3y^2)^(-2/3)?
4x^2y^2
ExplanationNegative exponent flips the fraction and cube root of 8x^3 is 2x.
#9
What is the simplified form of (√(x^2) * √(x^6)) / x?
x^4
ExplanationSimplify each square root, multiply, and divide by x.
#10
What is the simplified form of (27x^4)^(2/3)?
81x^2
ExplanationSquare root of 27 is 3, and exponent becomes x^(42/3) = x^2.
#11
What is the simplified form of (81x^9)^(1/2)?
9x^4.5
ExplanationSquare root of 81 is 9, and exponent becomes 9/2.
#12
What is the simplified form of (16x^6y^4)^(-1/2)?
2x^3y^2
ExplanationNegative exponent flips the fraction and square root cancels the exponent.
#13
What is the simplified form of (x^(-3/4) * y^(1/2))^2?
x^(3/2) * y^(1/2)
ExplanationSquare each term, and multiply the exponents.
#14
What is the simplified form of (x^(1/3) * y^(1/4))^6?
x^2 * y^(3/2)
ExplanationMultiply exponents by 6.
#15
What is the simplified form of (x^(3/2) * y^(1/3))^3?
x^4.5 * y
ExplanationMultiply each exponent by 3.
#16
What is the simplified form of (x^(5/3) * y^(1/4))^2?
x^(10/3) * y^(1/2)
ExplanationSquare each term and multiply the exponents.
#17
What is the simplified form of (x^(7/4) * y^(1/2))^4?
x^(7/4)y^2
ExplanationMultiply each exponent by 4.