Algebra 14.1-14.2 Review

Simplifying Radicals

100

Simplify the following radical expression

sqrt(98)

7sqrt2

200

Simplify the following radical expression

5sqrt(112)

20sqrt7

300

Simplify the following radical expression

sqrt(192xy^11z^6)

8y^5z^3sqrt(3xy)

400

Simplify the following radical expression

4root3(125x^9y^7)

20x^3y^2root3(y)

500

Simplify the following radical expression

root5(288x^3y^7)

2yroot5(9x^3y^2)

Radical Form to Exponential Form

100

Convert the following expression from Radical Form to Exponential Form

root5(n^4)

n^(4/5)

200

Convert the following expression from Radical Form to Exponential Form

root3(27m^2n^6)

3m^(2/3)n^2

300

Convert the following expression from Radical Form to Exponential Form

root4((5ab)^3)

5^(3/4)a^(3/4)b^(3/4)

OR

125^(1/4)a^(3/4)b^(3/4)

400

Convert the following expression from Radical Form to Exponential Form

root4(5ab^3)

5^(1/4)a^(1/4)b^(3/4)

500

Convert the following expression from Radical Form to Exponential Form and simplify

root4(32a^2b^14)

2^(5/4)a^(1/2)b^(7/2)

Exponential Form to Radical Form

100

Convert the following expression from Rational Exponents to Simplest Radical Form

x^(2/5)

root(5)(x^2)

(root(5)x)^2

200

Convert the following expression from Rational Exponents to Simplest Radical Form

7x^(2/3)

7root(3)x^2

7(root(3)x)^2

300

Convert the following expression from Rational Exponents to Simplest Radical Form

x^(17/2)

x^8sqrtx

400

Convert the following expression from Rational Exponents to Simplest Radical Form

(4x)^(5/2)

32x^2sqrtx

500

Convert the following expression from Rational Exponents to Simplest Radical Form

(12^3x)^(1/2)

24sqrt3x

Simplify

100

Simplify (-3y^1/3)(-2y^1/2) completely.

What is 6 6 root y to the 5th power?

200

Simplify (10xy)² over 20x²y completely.

What is 5y?

300

Simplify 12n⁸*5n⁵ over 4n¹¹.

What is 15n²?

400

Simplify 15m5n5*3n2 over 5mn.

What is 9m⁴n⁶?

500

Simplify 15j⁵k²*25j²k⁹ over (5jk)³ completely.

What is 3j⁴k⁸?

Negative Exponents

100

Simplify -4y over 2y to the power of 2/3

What is -2 3 root y to the power of 2?

200

The radical form of 8 to the -1/3 power.

What is -3 root 8?

300

The radical form of 7 to the -4/5 power

What is -5 root 7 to the 4th power?

400

The exponential form of -8 to the -6/7 power

What is -7 root -8 to the 6th power?

500

The exponential form of 9 to the -5/36 power

What is -36 root 9 to the 5th power?