Solving Radicals and Rational Exponents

Rational Exponents & Radicals

Important Vocabulary

Always has an invisible 2 on the outside unless told otherwise! This is called the "root".

2 = square root
3 = cubed root

Radical or "Square Root House"

​2

Rational Exponents:

• The numerator (top of the fraction) is the exponent on the inside of the "square root house"

• The denominator (bottom of the fraction) is the root, which will be on the outside.

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Multiple Choice

Change into radical form:

$$16^{\frac{1}{3}}$$

• $$\sqrt[3]{16}$$

• $$\sqrt[1]{16^3}$$

• $$\sqrt[16]{3}$$

• $$\sqrt[]{16^3}$$

Multiple Choice

Change into radical form:

$$25^{\frac{1}{2}}$$

• 25

• $$\frac{1}{25^2}$$

• $$\sqrt[2]{25}$$ or $$\sqrt[]{25}$$

• 17

Multiple Choice

Change into a rational exponent:

$$\sqrt[3]{125}$$

• 125³

• 125^1/3

• 5³

• 521

Multiple Choice

Change into a rational exponent:

$$\sqrt[3]{5^2}$$

• 52

• 5

• 5^2/3

• 5^3/2

Multiple Choice

Simplify into a whole number:

25^1/2

• 625

• 5

• 12.5

• 50

Multiple Choice

Simplify into a whole number:

16^1/2

• 32

• 256

• 4

• 8