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 ${10}^{-3}$

$(1^3+2^3+3^3+4^3{)}^{\frac{-3}{2}}=(1+8+27+64{)}^{\frac{-3}{2}}$
$=(100{)}^{\frac{-3}{2}}$
$=(100{)}^{\frac{1}{2}\times -3}$
$={\left[\right(100{)}^{\frac{1}{2}}]}^{-3}(\because (a^m{)}^n=a^{mn})$
$={10}^{-3}$