Math  /  Numbers & Operations

QuestionWrite the following in simplified radical form. 163\sqrt[3]{16}

Studdy Solution

STEP 1

1. We are given the expression 163\sqrt[3]{16}.
2. We need to express this in simplified radical form.

STEP 2

1. Express the number under the radical as a product of prime factors.
2. Simplify the radical expression using the properties of exponents.

STEP 3

Express 1616 as a product of prime factors.
16=24 16 = 2^4

STEP 4

Use the property of radicals that amn=am/n\sqrt[n]{a^m} = a^{m/n}.
163=243=24/3\sqrt[3]{16} = \sqrt[3]{2^4} = 2^{4/3}

STEP 5

Simplify 24/32^{4/3} by separating the integer and fractional parts of the exponent.
24/3=23/3×21/3=2×21/32^{4/3} = 2^{3/3} \times 2^{1/3} = 2 \times 2^{1/3}
The simplified radical form is:
2232\sqrt[3]{2}

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