Question 1
Which equation justifies why seven to the one third power equals the cube root of seven?
seven to the one third power all raised to the third power equals seven to the one third plus three power equals seven
seven to the one third power all raised to the third power equals seven to the three minus one third power equals seven
seven to the one third power all raised to the third power equals seven to the one third times three power equals seven
seven to the one third power all raised to the third power equals seven to the one third minus three power equals seven
Question 2(Multiple Choice Worth 1 points)
(03.01 LC)
Rewrite the expression with a rational exponent as a radical expression.
five to the three fourths power all raised to the two thirds power
the cube root of five squared
the twelfth root of five
the square root of five
the cube root of five the fourth power
Question 3(Multiple Choice Worth 1 points)
(03.01 MC)
Simplify square root of ten times square root of eight.
square root of eighteen
four square root of five
square root of eighty
eight square root of ten
Question 4(Multiple Choice Worth 1 points)
(03.01 MC)
Rewrite the expression with rational exponents as a radical expression by extending the properties of integer exponents.
y to the one third power all over y to the one sixth power
the square root of y to the one sixth power
the ninth root of y squared
the square root of y to the sixth power
the sixth root of y
Question 5(Multiple Choice Worth 1 points)
(03.01 MC)
Solve four square root of six plus eight square root of four and explain whether the answer is rational or irrational.
The answer twelve square root of ten is rational because the sum of a rational number and irrational number is a rational number.
The answer four square root of six plus sixteen is irrational because the sum of a rational number and irrational number is an irrational number.
The answer twelve square root of ten is irrational because the sum of a rational number and irrational number is an irrational number.
The answer four square root of six plus sixteen is rational because the sum of a rational number and irrational number is a rational number.
Question 6(Multiple Choice Worth 1 points)
(03.01 MC)
Simplify seven square root of three end root minus four square root of six end root plus square root of forty eight end root minus square root of fifty four.
eleven square root of six end root minus seven square root of twelve
eleven square root of three end root minus seven square root of six
negative three square root of nine
four square root of nine
Question 7(Multiple Choice Worth 1 points)
(03.01 MC)
Explain how the Quotient of Powers Property was used to simplify this expression.
three to the fourth power all over nine equals three squared
By simplifying 9 to 32 to make both powers base three and adding the exponents
By simplifying 9 to 32 to make both powers base three and subtracting the exponents
By finding the quotient of the bases to be one third and simplifying the expression
By finding the quotient of the bases to be one third and cancelling common factors
Question 8(Multiple Choice Worth 1 points)
(03.01 LC)
Rewrite the radical expression as an expression with a rational exponent.
the fourth root of seven to the fifth power
seven to the five fourths power
x20
x
seven to the four fifths power
Question 9(Multiple Choice Worth 1 points)
(03.01 MC)
Given the algebraic expression the quantity 125 times x to the seven-thirds power end quantity to the negative one-third power comma, create an equivalent expression.
5 times x to the seven-ninths power
5x2
1 divided by the quantity 5 times x to the seven-ninths power end quantity
1 divided by the quantity 5 times x squared end quantity
Question 10(Multiple Choice Worth 1 points)
(03.01 MC)
Simplify square root of five times the quantity six minus four square root of three.
9
thirty square root of three
six square root of five minus four square root of fifteen
square root of thirty minus twenty square root of three
answer each question seperately
Question 1:
The equation that justifies why seven to the one third power equals the cube root of seven is: "seven to the one third power all raised to the third power equals seven to the one third plus three power equals seven."
Question 2:
The rational exponent expression "five to the three fourths power all raised to the two thirds power" can be rewritten as "the cube root of five squared."
Question 3:
The square root of ten times the square root of eight simplifies to "four square root of five."
Question 4:
The expression "y to the one third power all over y to the one sixth power" can be rewritten as "the square root of y to the one sixth power."
Question 5:
The sum of "four square root of six plus eight square root of four" simplifies to "twelve square root of ten," and it is rational because the sum of a rational number and an irrational number is a rational number.
Question 6:
The expression "seven square root of three end root minus four square root of six end root plus square root of forty eight end root minus square root of fifty four" simplifies to "eleven square root of three end root minus seven square root of six."
Question 7:
The Quotient of Powers Property was used to simplify the expression by simplifying 9 to 32 to make both powers have a base of three and subtracting the exponents.
Question 8:
The radical expression "the fourth root of seven to the fifth power" can be rewritten as "seven to the five fourths power."
Question 9:
The equivalent expression for "the quantity 125 times x to the seven-thirds power end quantity to the negative one-third power" is "1 divided by the quantity 5 times x to the seven-ninths power end quantity."
Question 10:
The expression "square root of five times the quantity six minus four square root of three" simplifies to "six square root of five minus four square root of fifteen."
Question 1:
The equation that justifies why seven to the one third power equals the cube root of seven is: "seven to the one third power all raised to the third power equals seven to the one third plus three power equals seven."
Question 2:
The rational exponent expression "five to the three fourths power all raised to the two thirds power" can be rewritten as "the cube root of five squared."
Question 3:
The square root of ten times the square root of eight simplifies to "four square root of five."
Question 4:
The expression "y to the one third power all over y to the one sixth power" can be rewritten as "the square root of y to the one sixth power."
Question 5:
The sum of "four square root of six plus eight square root of four" simplifies to "twelve square root of ten," and it is rational because the sum of a rational number and an irrational number is a rational number.
Question 6:
The expression "seven square root of three end root minus four square root of six end root plus square root of forty eight end root minus square root of fifty four" simplifies to "eleven square root of three end root minus seven square root of six."
Question 7:
The Quotient of Powers Property was used to simplify the expression by simplifying 9 to 32 to make both powers have a base of three and subtracting the exponents.
Question 8:
The radical expression "the fourth root of seven to the fifth power" can be rewritten as "seven to the five fourths power."
Question 9:
The equivalent expression for "the quantity 125 times x to the seven-thirds power end quantity to the negative one-third power" is "1 divided by the quantity 5 times x to the seven-ninths power end quantity."
Question 10:
The expression "square root of five times the quantity six minus four square root of three" simplifies to "six square root of five minus four square root of fifteen."
write answers in equation form
Question 1:
The equation is: (7^(1/3))^3 = 7^(1/3)
Question 2:
The equation is: ((5^(3/4))^2)^(2/3) = 5^(2/3)
Question 3:
The equation is: √10 * √8 = √80 = 4√5
Question 4:
The equation is: (y^(1/3)) / (y^(1/6)) = y^((1/3) - (1/6)) = y^(1/6)
Question 5:
The sum is: 4√6 + 8√4 = 12√10
And the answer is rational.
Question 6:
The expression is: 7√3 - 4√6 + √48 - √54
And it simplifies to: 11√3 - 7√6
Question 7:
The equation is: 3^4 / 9 = 3^(2-1) = 3^1 = 3^2
Question 8:
The expression is: (7^(1/4))^5
And it can be rewritten as: 7^(5/4)
Question 9:
The given expression is: (125 * x^(7/3))^(-1/3)
The equivalent expression is: 1 / (5 * x^(7/9))
Question 10:
The expression is: √5 * (6 - 4√3)
And it simplifies to: 6√5 - 4√15
Answer for Question 1:
The equation that justifies why seven to the one third power equals the cube root of seven is: seven to the one third power all raised to the third power equals seven.
Answer for Question 2:
The expression "five to the three fourths power all raised to the two thirds power" can be rewritten as "the cube root of five squared."
Answer for Question 3:
The simplified form of "square root of ten times square root of eight" is "four square root of five."
Answer for Question 4:
The expression "y to the one third power all over y to the one sixth power" can be rewritten as "the square root of y to the sixth power."
Answer for Question 5:
The answer to "four square root of six plus eight square root of four" is "twelve square root of ten." The answer is rational because the sum of a rational number and an irrational number is a rational number.
Answer for Question 6:
The simplified form of "seven square root of three end root minus four square root of six end root plus square root of forty eight end root minus square root of fifty four" is "eleven square root of three end root minus seven square root of six."
Answer for Question 7:
The Quotient of Powers Property was used to simplify the expression "three to the fourth power divided by nine equals three squared." The property states that when dividing powers with the same base, you subtract the exponents. In this case, 4 - 2 equals 2.
Answer for Question 8:
The radical expression "the fourth root of seven to the fifth power" can be rewritten as "seven to the five fourths power."
Answer for Question 9:
An equivalent expression to "the quantity 125 times x to the seven-thirds power end quantity to the negative one-third power" is "1 divided by the quantity 5 times x to the seven-ninths power end quantity."
Answer for Question 10:
The simplified form of "square root of five times the quantity six minus four square root of three" is "six square root of five minus four square root of fifteen."