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Simplify

Question:

Simplify

(i) $2^{\frac{2}{3}} \times 2^{\frac{1}{3}}$

(ii) $2^{\frac{2}{3}} \times 2^{\frac{1}{5}}$

(iii) $7^{\frac{5}{6}} \times 7^{\frac{2}{3}}$

(iv) $(1296)^{\frac{1}{4}} \times(1296)^{\frac{1}{2}}$

 

Solution:

(i) $2^{\frac{2}{3}} \times 2^{\frac{1}{3}}$

$2^{\frac{2}{3}} \times 2^{\frac{1}{3}}=2^{\frac{2}{3}+\frac{1}{3}}$

$=2^{\frac{2+1}{3}}$

$=2^{\frac{3}{3}}$

$=2^{1}$

$=2$

(ii) $2^{\frac{2}{3}} \times 2^{\frac{1}{5}}$

$2^{\frac{2}{3}} \times 2^{\frac{1}{5}}=2^{\frac{2}{3}+\frac{1}{5}}$

$=2^{\frac{10+3}{15}}$

$=2^{\frac{13}{15}}$

(iii) $7^{\frac{5}{6}} \times 7^{\frac{2}{3}}$

$7^{\frac{5}{6}} \times 7^{\frac{2}{3}}=7^{\frac{5}{6}}+\frac{2}{3}$

$=7^{\frac{5+4}{6}}$

$=7^{\frac{9}{6}}$

$=7^{\frac{3}{2}}$

(iv) $(1296)^{\frac{1}{4}} \times(1296)^{\frac{1}{2}}$

$(1296)^{\frac{1}{4}} \times(1296)^{\frac{1}{2}}=(1296)^{\frac{1}{4}+\frac{1}{2}}$

$=(1296)^{\frac{1+2}{4}}$

$=(1296)^{\frac{3}{4}}$

$=\left((6)^{4}\right)^{\frac{3}{4}}$

$=(6)^{3}$

$=216$

 

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