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(a) Find the value of $16^{rac{1}{4}}$ (b) Simplify $\sqrt{(2x)^{\frac{1}{4}}}$ - Edexcel - A-Level Maths Pure - Question 3 - 2011 - Paper 2

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$(a)-Find-the-value-of-$16^{-rac{1}{4}}$----(b)-Simplify-$\sqrt{(2x)^{\frac{1}{4}}}$-Edexcel-A-Level Maths Pure-Question 3-2011-Paper 2.png$

(a) Find the value of $16^{rac{1}{4}}$ (b) Simplify $\sqrt{(2x)^{\frac{1}{4}}}$

Worked Solution & Example Answer:(a) Find the value of $16^{rac{1}{4}}$ (b) Simplify $\sqrt{(2x)^{\frac{1}{4}}}$ - Edexcel - A-Level Maths Pure - Question 3 - 2011 - Paper 2

Step 1

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Answer

To find the value of $16^{\frac{1}{4}}$ , we can rewrite 16 as a power of 2:

$16 = 2^4.$
Now substituting this into the equation gives:

$16^{\frac{1}{4}} = (2^4)^{\frac{1}{4}} = 2^{4 \times \frac{1}{4}} = 2^1 = 2.$
Thus, the answer is (2).

Step 2

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Answer

To simplify $\sqrt{(2x)^{\frac{1}{4}}}$ , we can rewrite the square root as an exponent:

$\sqrt{(2x)^{\frac{1}{4}}} = (2x)^{\frac{1}{4} \times \frac{1}{2}} = (2x)^{\frac{1}{8}}.$
This can be separated into:

$(2x)^{\frac{1}{8}} = 2^{\frac{1}{8}} \cdot x^{\frac{1}{8}}.$
Thus, the simplified expression is (2^{\frac{1}{8}} x^{\frac{1}{8}}).

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