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Show that \( \frac{\sqrt[3]{81}}{3} \) can be written as \( 3^{1} \). - OCR - GCSE Maths - Question 17 - 2017 - Paper 1

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Question 17

Show-that-\(-\frac{\sqrt[3]{81}}{3}-\)-can-be-written-as-\(-3^{1}-\).-OCR-GCSE Maths-Question 17-2017-Paper 1.png

Show that \( \frac{\sqrt[3]{81}}{3} \) can be written as \( 3^{1} \).

Worked Solution & Example Answer:Show that \( \frac{\sqrt[3]{81}}{3} \) can be written as \( 3^{1} \). - OCR - GCSE Maths - Question 17 - 2017 - Paper 1

Step 1

Step 1: Calculate \( \sqrt[3]{81} \)

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Answer

First, we find the cube root of 81. Since ( 81 = 3^4 ), we can rewrite it as:

813=343=34/3\sqrt[3]{81} = \sqrt[3]{3^4} = 3^{4/3}

Step 2

Step 2: Substitute into the original expression

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Answer

Now we substitute ( \sqrt[3]{81} ) back into the expression:

8133=34/33\frac{\sqrt[3]{81}}{3} = \frac{3^{4/3}}{3}

Step 3

Step 3: Simplify the expression

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Answer

Next, we simplify the division by expressing ( 3 ) as ( 3^{1} ):

34/331=34/3−1=34/3−3/3=31/3\frac{3^{4/3}}{3^{1}} = 3^{4/3 - 1} = 3^{4/3 - 3/3} = 3^{1/3}

Therefore, we have:

31/3=313^{1/3} = 3^{1}, as required.

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