Express each of the following products as a monomials and verify the r

1.	Express each of the following products as a monomials and verify the result for x=1, y= 2:\((\frac{1}{8}x^2y^4)\times (\frac{1}{4}x^4y^2)\times (xy)\times 5\)
Answer» \(\frac{1}{8}\) × \(\frac{1}{4}\) × 5 × x² × x⁴ × x × y⁴ × y² × y = \(\frac{5}{32}\) × x⁶ × y⁶ = \(\frac{5}{32}\)x⁶y⁶ Verification: When x = 1 and y = 2 R.H.S = \(\frac{5}{32}\) × 1⁶ × 2⁶ = \(\frac{5}{32}\) × 64 = 5 × 2 = 10 L.H.S = \(\frac{1}{8}\) × 1² × 2⁴ × \(\frac{1}{4}\) × 1⁴ × 2² × 1 × 2 × 5 = 10 Therefore, L.H.S = R.H.S

Express each of the following products as a monomials and verify the result for x=1, y= 2:\((\frac{1}{8}x^2y^4)\times (\frac{1}{4}x^4y^2)\times (xy)\times 5\)

Answer»

\(\frac{1}{8}\) × \(\frac{1}{4}\) × 5 × x² × x⁴ × x × y⁴ × y² × y

= \(\frac{5}{32}\) × x⁶ × y⁶

= \(\frac{5}{32}\)x⁶y⁶

Verification:

When x = 1 and y = 2

R.H.S = \(\frac{5}{32}\) × 1⁶ × 2⁶

= \(\frac{5}{32}\) × 64

= 5 × 2

= 10

L.H.S = \(\frac{1}{8}\) × 1² × 2⁴ × \(\frac{1}{4}\) × 1⁴ × 2² × 1 × 2 × 5

= 10

Therefore,

L.H.S = R.H.S