find the value of each of the following a.16^-3/4,3√2.4√2^12√36,15√6+√216,11^5/2/11^3/2,5^3/2 7^3/2,√162√2,(8+√3)/(8-√3)
Answers
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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