Find the value of (a) $25^{\frac{1}{2}}$ (b) $25^{-\frac{3}{2}}$ - Edexcel - A-Level Maths Pure - Question 3 - 2011 - Paper 1

To evaluate $25^{-\frac{3}{2}}$, we first consider the reciprocal of the base raised to the positive exponent:

$25^{-\frac{3}{2}} = \frac{1}{25^{\frac{3}{2}}}.$

Now, we compute $25^{\frac{3}{2}}$:

$25^{\frac{3}{2}} = (25^{\frac{1}{2}})^3 = (\sqrt{25})^3 = 5^3 = 125.$

Substituting this back, we get:

$25^{-\frac{3}{2}} = \frac{1}{125}.$

So, the answer is $\frac{1}{125}$ or $0.008$.