Question

Simplify {(125)^1/3 x (25)^1/2 +(16)^3/4 x(64)^1/3 + 1/(49)^-1/2}^-2/3

Answer 1

Answer:
`(1)/(5^(4)/(3) +2^(10)/(3) +7^(2)/(3) )`

Step-by-step explanation:

1- Factorize all numbers : 125=5³; 25=5²; 16=
`2^(4)`;64=
`2^(6)`; 49=7²

2- Write all the thing factorized: {(5³)
`(1)/(3)`×(5²)
`(1)/(2)`+(
`2^(4)`)
`(3)/(4)`×(
`2^(6)`)
`(1)/(3)`+1/(7²)
`-(1)/(2)`}
`-(2)/(3)`=

3-Multiply all the potences per the fractions outside the parentesis: (5×5+2³×2²+7)
`-(2)/(3)`=

4-Put toghether all the same bases: (5²+
`2^(5)`+7)
`-(2)/(3)`=

5-Multiply all the potences for the fraction outside the parentesis:

5
`-(4)/(3)`+2
`-(10)/(3)`+7
`-(2)/(3)`=

6-You can leave the equation like this (with negative potences) or if you prefer it put a 1 on the top and divide the numbers:

`(1)/(5^(4)/(3) +2^(10)/(3) +7^(2)/(3) )`

Answer 2

Hi,

Explanation:

`\{(125)^(1/3) * (25)^(1/2) +(16)^(3/4) *(64)^(1/3) + 1/(49)^(-1/2) \}^(-2/3)\\\\=(\sqrt[3]{125}* √(25)+\sqrt[4]{16^3}+√(49) )^ {-2/3}\\\\=(5*5+8*4+7)^(-2/3)\\\\=64^(-2/3)\\\\=(1)/(64^(2/3))\\\\=(1)/(2^(12/3))\\\\=(1)/(2^4)\\\\\boxed{=(1)/(16)}\\`

=0,0625