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Express $8^{2x+3}$ in the form $2^y$, stating $y$ in terms of $x$. - Edexcel - A-Level Maths Pure - Question 5 - 2013 - Paper 3

Question 5

$Express-$8^{2x+3}$-in-the-form-$2^y$,-stating-$y$-in-terms-of-$x$.-Edexcel-A-Level Maths Pure-Question 5-2013-Paper 3.png$

Express $8^{2x+3}$ in the form $2^y$, stating $y$ in terms of $x$.

Worked Solution & Example Answer:Express $8^{2x+3}$ in the form $2^y$, stating $y$ in terms of $x$. - Edexcel - A-Level Maths Pure - Question 5 - 2013 - Paper 3

Step 1

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Answer

We know that $8$ can be expressed as a power of $2$ : $8 = 2^3$ . Therefore, we can rewrite the expression as:

$8^{2x+3} = (2^3)^{2x+3}$

Step 2

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Answer

Using the power of a power rule, which states that $(a^m)^n = a^{m \cdot n}$ , we can rewrite the expression as:

$(2^3)^{2x+3} = 2^{3(2x+3)} = 2^{6x + 9}$

Step 3

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101 rated

Answer

From the expression $2^{6x + 9}$ , we can identify that in the form of $2^y$ , we have:

$y = 6x + 9$

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