Question

\left(-7\right)^{\frac{5}{3}}\left(\frac{1}{56}\right)^{\frac{5}{3}}

Answer 1

`=\left(-7\right)^{(5)/(3)}* \frac{1}{224\:* \:7^{(2)/(3)}}`

Explanation:

Re-arrange

`\left((1)/(56)\right)^{(5)/(3)}=\frac{1^{(5)/(3)}}{56^{(5)/(3)}}\\=\left(-7\right)^{(5)/(3)}\frac{1^{(5)/(3)}}{56^{(5)/(3)}}\\56^{(5)/(3)}=224 * 7^{(2)/(3) }`

↑ Following step was found by converting to improper fraction

Therefore,

`\left(-7\right)^{(5)/(3)}\frac{1^{(5)/(3)}}{224\cdot \:7^{(2)/(3)}}`

Remember the exponents rule if the whole number is equal to one

`1^x=1\\1^{(5)/(3)}=1`

And this rule would also play into the equation.

`\left(-7\right)^{(5)/(3)}* \frac{1}{224\cdot \:7^{(2)/(3)}}`

Hope this helps!