Question

Evaluate $(1^3+2^3+3^3+4^3{)}^{\frac{-3}{2}}.$

• A. ${10}^{-1}$
• B. ${10}^{-2}$
• C. ${10}^{-3}$
• D. ${10}^{-4}$

Answer 1

The correct option is C

${10}^{-3}$

$(1^3+2^3+3^3+4^3{)}^{\frac{-3}{2}}$
$=(1+8+27+64{)}^{\frac{-3}{2}}$
$=(100{)}^{\frac{-3}{2}}$

$=({10}^2{)}^{\frac{-3}{2}}$

$\because (a^m{)}^n=(a{)}^{m\times n}$
$\Rightarrow (10{)}^{2\times \frac{-3}{2}}={10}^{-3}$