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Find the value of $8^{\frac{4}{3}}$ - Edexcel - A-Level Maths Pure - Question 3 - 2007 - Paper 1

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Find the value of $8^{\frac{4}{3}}$. (b) Simplify $ \frac{15x^{\frac{4}{3}}}{3x} $.

Worked Solution & Example Answer:Find the value of $8^{\frac{4}{3}}$ - Edexcel - A-Level Maths Pure - Question 3 - 2007 - Paper 1

Step 1

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Answer

To find the value of $8^{\frac{4}{3}}$ , we can first express 8 as a power of 2:

$8 = 2^3$

Therefore:

$8^{\frac{4}{3}} = (2^3)^{\frac{4}{3}}$

Using the power of a power property of exponents, we get:

$(2^3)^{\frac{4}{3}} = 2^{3 \cdot \frac{4}{3}} = 2^4$

Thus:

$2^4 = 16$

So, the value of $8^{\frac{4}{3}}$ is 16.

Step 2

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Answer

To simplify the expression ( \frac{15x^{\frac{4}{3}}}{3x} ), we can start by dividing the coefficients and simplifying the variables:

Divide the coefficients: $\frac{15}{3} = 5$
For the variable part, we have: $\frac{x^{\frac{4}{3}}}{x} = x^{\frac{4}{3} - 1} = x^{\frac{4}{3} - \frac{3}{3}} = x^{\frac{1}{3}}$

So the expression simplifies to:

$5x^{\frac{1}{3}}$

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