Question

simplify the following
$(xy ^{2} ) ^{4} .(x {}^{2} y) {}^{4}$


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Answer 1

Answer:

(xy²)⁴ × (x²y)⁴ = (xy)¹²

Step-by-step explanation:

Before solving these kinds of problems we must know certain important result.

1. (ab)^m = (a^m) × (b^m)

2. (a^m) × (a^n) = a^(m + n)

3. (a^m)^n = a^(m × n) = a^(mn)

4. (a^m) × (b^m) = (a × b)^m

So, now let's solve it,

(xy²)⁴ × (x²y)⁴

= (x⁴y^(2 × 4)) × (x^(2 × 4)y⁴)

= (x⁴y⁸) × (x⁸y⁴)

= x⁴ × x⁸ × y⁸ × y⁴

= x^(8 + 4) × y^(8 + 4)

= x¹² × y¹²

= (xy)¹²

OR

(xy²)⁴ × (x²y)⁴

= (xy² × x²y)⁴

= (x × x² × y² × y)⁴

= (x^(1 + 2) × y^(1 + 2))⁴

= (x³y³)⁴

= ((xy)³)⁴

= (xy)^(3 × 4)

= (xy)¹²

Thus,

(xy²)⁴ × (x²y)⁴ = (xy)¹²

Hope it helped and you understood it........All the best