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

Answer:

(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.

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

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

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