Question

Help meh please because I don’t understand this

Answer 1

`\textsf{a) \quad $(2)/(5)$}`

`\textsf{b) \quad $(5)/(2)$}`

Explanation:

Question a)

Given expression:

`\left((4)/(25)\right)^{(1)/(2)}`

Rewrite 4 as 2² and 25 as 5²:

`\implies \left((2^2)/(5^2)\right)^{(1)/(2)}`

`\textsf{Apply the exponent rule} \quad \left((a)/(b)\right)^c=(a^c)/(b^c):`

`\implies \frac{(2^2)^{(1)/(2)}}{(5^2)^{(1)/(2)}}`

`\textsf{Apply the exponent rule} \quad (a^b)^c=a^(bc):`

`\implies \frac{2^{(2\cdot(1)/(2))}}{5^{(2\cdot(1)/(2))}}`

`\implies (2^1)/(5^1)`

`\implies (2)/(5)`

Question b)

Given expression:

`\left((4)/(25)\right)^{-(1)/(2)}`

Rewrite 4 as 2² and 25 as 5²:

`\implies \left((2^2)/(5^2)\right)^{-(1)/(2)}`

`\textsf{Apply the exponent rule} \quad \left((a)/(b)\right)^c=(a^c)/(b^c):`

`\implies \frac{(2^2)^{-(1)/(2)}}{(5^2)^{-(1)/(2)}}`

`\textsf{Apply the exponent rule} \quad (a^b)^c=a^(bc):`

`\implies \frac{2^{(2\cdot -(1)/(2))}}{5^{(2\cdot -(1)/(2))}}`

`\implies (2^(-1))/(5^(-1))`

`\textsf{Apply the exponent rule} \quad a^(-n)=(1)/(a^n):`

`\implies (1)/(2^1 \cdot 5^(-1))`

`\implies (1)/(2 \cdot 5^(-1))`

`\textsf{Apply the exponent rule} \quad (1)/(a^(-n))=a^n:`

`\implies (5^1)/(2)`

`\implies (5)/(2)`