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Show that $ rac{ oot{3}{a}}{a^{ rac{1}{3}}}$ can be expressed as $a^{ rac{n}{3}}$. - OCR - GCSE Maths - Question 17 - 2019 - Paper 1

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Question 17

Show-that-$-rac{-oot{3}{a}}{a^{-rac{1}{3}}}$-can-be-expressed-as-$a^{-rac{n}{3}}$.-OCR-GCSE Maths-Question 17-2019-Paper 1.png

Show that $ rac{ oot{3}{a}}{a^{ rac{1}{3}}}$ can be expressed as $a^{ rac{n}{3}}$.

Worked Solution & Example Answer:Show that $ rac{ oot{3}{a}}{a^{ rac{1}{3}}}$ can be expressed as $a^{ rac{n}{3}}$. - OCR - GCSE Maths - Question 17 - 2019 - Paper 1

Step 1

Step 1: Express $ rac{ oot{3}{a}}{a^{ rac{1}{3}}}$ in terms of exponents

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Answer

Begin by rewriting the expression using the properties of exponents. Recall that oot{3}{a} = a^{ rac{1}{3}}, so we can rewrite the expression as: a13a13\frac{a^{\frac{1}{3}}}{a^{\frac{1}{3}}}

Step 2

Step 2: Simplify the expression

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Answer

Using the law of exponents, rac{a^m}{a^n} = a^{m-n}, we can simplify the expression further: a13−13=a0a^{\frac{1}{3} - \frac{1}{3}} = a^0

Step 3

Step 3: Final result

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Answer

Thus, we have shown that \root3aa13=a0\frac{\root{3}{a}}{a^{\frac{1}{3}}} = a^{0}, which can also be expressed as an3a^{\frac{n}{3}} for n=0n = 0.

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