# Find the value of each of the following: ​(i) 16^(1/4) (ii) 625^(-3/4)

(1) 16(1/4)

16(1/4) can be written as

16(1/4) = (44)(1/4)

The laws of exponents are tabulated below.

 am.an=am+n (am)n = amn (ab)n = an bn (a/b)n = an/bn am/an = am-n am/an = 1/an-m

So (44)1/4 can be written as

= 2(4 × 1/4)

= 21

(16)1/4 = 2

(2) 625(-3/4)

Since the exponent given is negative, it must be converted into a fraction.

$625^{\left ( \frac{-3}{4} \right )} = \left ( \frac{1}{625} \right )^{\frac{3}{4}}$ $\left ( \frac{1}{625} \right )^{\frac{3}{4}} = \left \{ \left ( \frac{1}{625} \right )^{\frac{1}{4}} \right \}^{3}$ $\left ( \frac{1}{625} \right )^{\frac{3}{4}} = \left ( \frac{1}{5} \right )^{3}$

$\left ( \frac{1}{625} \right )^{\frac{3}{4}} = \frac{1}{125}$