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Laws of Exponents for Real Numbers

Expand 5x2+...

Question

Expand $\frac{5 x^{2} + 4 x + 7}{{(2 x + 3)}^{\frac{3}{2}}}$

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Solution

Given
$\frac{5 x^{2} + 4 x + 7}{(2 x + 3)^{\frac{3}{2}}}$
Applying exponent rule
$(a)^{b + c} = a^{b} . a^{c}$
$(2 x + 3)^{\frac{3}{2}} = (2 x + 3)^{1 + \frac{1}{2}} = (2 x + 3) \sqrt{2 x + 3}$
$= \frac{5 x^{2} + 4 x + 7}{(2 x + 3) \sqrt{2 x + 3}}$

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