Question

simplify 64^-1/3(64^1/3-64^2/3)

Answer 1

Answer:

$64^{-\frac{1}{3}}(64^{\frac{1}{3}}-64^{\frac{2}{3}})=-3$

Step-by-step explanation:

Given : Expression $64^{-\frac{1}{3}}(64^{\frac{1}{3}}-64^{\frac{2}{3}})$

To find : Simplify the expression ?

Solution :

We know that, $64=4^3$

Replace that,

$=(4^3)^{-\frac{1}{3}}((4^3)^{\frac{1}{3}}-(4^3)^{\frac{2}{3}})$

Applying exponent identity, $(a^b)^x=a^{b\times x}$

$=(4)^{-\frac{3}{3}}((4)^{\frac{3}{3}}-(4)^{\frac{2\times 3}{3}})$

$=(4)^{-1}((4)^{1}-(4)^{2})$

$=(4)^{-1}(4-16)$

$=\frac{1}{4}\times(-12)$

$=-3$

Therefore, $64^{-\frac{1}{3}}(64^{\frac{1}{3}}-64^{\frac{2}{3}})=-3$

Answer 2

Answer:

-3

Step-by-step explanation:

64^-1/3(64^1/3-64^2/3)=-3