Exponents — Maths STD 7 — Question

$(8^4+8^2)^{\frac{1}{2}}$
$=(8^{2+2}+8^2)^{\frac{1}{2}}$
$=(8^2\times8^2+8^2)^{\frac{1}{2}}$ $(\text{As},\text{x}^{\text{m+n}}=\text{x}^{\text{m}}\times\text{x}^{\text{n}})$
$=[8^2\times(8^2+1)]^{\frac{1}{2}}$ $[\text{As}, \text{ab+ac}=\text{a}\times(\text{a+c})]$
$=(8^2)^{\frac{1}{2}}\times(8^2+1)^{\frac{1}{2}}$ $[\text{As, }(\text{ab})^{\text{m}}=\text{a}^{\text{m}}\times\text{b}^{\text{m}}]$
$=8^{2\times\frac{1}{2}}\times(64+1)^{\frac{1}{2}}$
$=8\times65^{\frac{1}{2}}$
$=8\sqrt{65}$
Hence, the correct alternative is option $(d).$