Question

Expand the algebraic expression $a^{\frac{1}{3}}(a^{\frac{3}{2}}+a^3)$

• A. $a^{\frac{11}{6}}+a^{\frac{10}{3}}$
• B. $a^{\frac{11}{6}}+a^{\frac{7}{3}}$
• C. $a^{\frac{7}{6}}+a^{\frac{10}{3}}$
• D. $a^{\frac{5}{6}}+a^{\frac{10}{3}}$

Answer 1

The correct option is A $a^{\frac{11}{6}}+a^{\frac{10}{3}}$

$a^{\frac{1}{3}}(a^{\frac{3}{2}}+a^3)=a^{\frac{1}{3}}\cdot a^{\frac{3}{2}}+a^{\frac{1}{3}}\cdot a^3$
Using Distributive property of multiplication
$=a^{\frac{1}{3}+\frac{3}{2}}+a^{\frac{1}{3}+\left(3\right)}$
Applying laws of exponents
$=a^{\frac{2}{6}+\frac{9}{6}}+a^{\frac{1}{3}+\frac{9}{3}}$
$=a^{\frac{11}{6}}+a^{\frac{10}{3}}(a\ne 0)$