Question

$9^{\frac{3}{2}}\times (243{)}^{\frac{2}{3}}$ simplifies to

• A. $3^{\frac{10}{3}}$
• B. $3^{\frac{19}{3}}$
• C. $3^{\frac{1}{3}}$
• D. $3^{19}$

Answer 1

Answer: (B)

$3^{\frac{19}{3}}$

we know that,

$\because (a^m{)}^n=a^{mn}$

so

$9^{\frac{3}{2}}=(3^2{)}^{\frac{3}{2}}$

$=3^3$

we know that

$243=3^5$

so,

$(3^5{)}^{\frac{2}{3}}$

$=3^{\frac{10}{3}}$

now,

we know

$\because a^m\times a^n=a^{m+n}$

so, $3^{\frac{10}{3}}\times 3^3=3^{\frac{10}{3}+3}$

$=3^{\frac{19}{3}}$