A-Level Edexcel Maths Pure Differentiation: 2. (a) Evaluate $igg(32^{rac{2

2. (a) Evaluate $igg(32^{rac{2}{3}}igg)$, giving your answer as an integer - Edexcel - A-Level Maths Pure - Question 4 - 2012 - Paper 2

Question 4

$2.-(a)-Evaluate-$igg(32^{-rac{2}{3}}igg)$,-giving-your-answer-as-an-integer-Edexcel-A-Level Maths Pure-Question 4-2012-Paper 2.png$

2. (a) Evaluate $igg(32^{rac{2}{3}}igg)$, giving your answer as an integer. (b) Simplify fully $igg(rac{25x^{rac{1}{2}}}{4}igg)$.

Worked Solution & Example Answer:2. (a) Evaluate $igg(32^{rac{2}{3}}igg)$, giving your answer as an integer - Edexcel - A-Level Maths Pure - Question 4 - 2012 - Paper 2

Step 1

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Answer

To evaluate $igg(32^{ rac{2}{3}}igg)$ , we first express 32 as a power of 2:

$32 = 2^5$

Thus, we can substitute:

$32^{ rac{2}{3}} = (2^5)^{ rac{2}{3}}$

Using the power of a power property, this is:

$= 2^{5 imes rac{2}{3}} = 2^{ rac{10}{3}}$

Now, we can rewrite this as:

$= 2^{3 + rac{1}{3}} = 2^3 \times 2^{ rac{1}{3}}$

Calculating $2^3$ gives:

$2^3 = 8$

Now evaluating $2^{ rac{1}{3}}$ gives us the cubic root of 2, but since the question asks for an integer, we keep our answer as:

$8$ .

Step 2

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Answer

To simplify $igg( rac{25x^{ rac{1}{2}}}{4}igg)$ , we start by recognizing that:

$25 = 5^2$

Thus, we can rewrite the expression as:

$rac{5^2 x^{ rac{1}{2}}}{4}$

Next, we know that $4 = 2^2$ , so we can rewrite it as:

$rac{5^2 x^{ rac{1}{2}}}{2^2}$

Now we can simplify the expression as:

$rac{5^2}{2^2} \times x^{ rac{1}{2}} = rac{25}{4} \times x^{ rac{1}{2}}$

Alternatively, simplifying gives:

$= rac{25 \sqrt{x}}{4}$

Thus, the fully simplified answer is:

$rac{25 \sqrt{x}}{4}$ .