√169x^6 (Solve for points)?

Question

I still don't understand. If the √169x^2 is 13x then what is √169x^6 ? Why did the power change?

Answer 1

The value of √(169x²) = 13x  → (1).

√(169x⁶)

= √(169x^{(2 + 4)})

Product of powers property : a^{(b + c)} = a^b × a^c , where a, b, and c are all real numbers.

= √(169x² * x⁴)

Apply formula : √(a *  b) = √a * √b.

= √(169x²) * √x⁴

= 13x * x²                (From eq (1))

= 13x³ .

∴ √(169x⁶) = 13x³ .