Question

Simplify: 64-⅓ (64⅓ - 64⅔)

Answer 1

Answer:

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

Step-by-step explanation:

we have to simplify the following,

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

we use the following law of exponent,

$(x^a)^b=x^{a\times b}\:\:and\:\:x^a\times x^b=x^{a+b}$

in exponent form we write 64 = $2^6$

$\implies(2^6)^{\frac{-1}{3}}((2^6)^{\frac{1}{3}}-(2^6)^{\frac{2}{3}})$

$\implies2^{6\times\frac{-1}{3}}(2^{6\times\frac{1}{3}}-2^{6\times\frac{2}{3}})$

$\implies2^{-2}(2^{2}-2^{4})$

$\implies2^{-2}\times2^2(1-2^2)$

$\implies2^{-2+2}(1-4)$

$\implies-3$

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

Answer 2

643−1(6431−6432)is−3

Step-by-step explanation:

we have to simplify the following,

$64^{\frac{-1}{3}}(64^{\frac{1}$

${3}}-64^{\frac{2}{3}})643−1(6431−6432)$

we use the following law of exponent,

$(x^a)^b=x^{a\times b}\:\:and\:\:x^a\times x^b=x^{a+b}(xa)b=xa×bandxa×xb=xa+b$

in exponent form we write $64 = 2^626$

$\implies(2^6)^{\frac{-1}{3}}((2^6)^{\frac{1}{3}}-(2^6)^{\frac{2}{3}})⟹(26)3−1((26)31−(26)32)$

$\implies2^{6\times\frac{-1}{3}}(2^{6\times\frac{1}{3}}-2^{6\times\frac{2}{3}})⟹26×3−1(26×31−26×32)</p><p>\implies2^{-2}(2^{2}-2^{4})⟹2−2(22−24)</p><p>\implies2^{-2}\times2^2(1-2^2)⟹2−2×22(1−22)</p><p>\implies2^{-2+2}(1-4)⟹2−2+2(1−4)</p><p>\implies-3⟹−3</p><p>Therefore, [tex]64^{\frac{-1}{3}}(64^{\frac{1}{3}}-64^{\frac{2}{3}})\:\:is\:\:-3643−1(6431−6432)is−3$