Simplify: ((2xy2)3 (4x3y)2) / (42x10y2 2x4y4)

Question

ScanSolve AI Tutor · Accepted Answer

Okay, merro, let's simplify this expression.

Question 2.4 Simplify $\frac{(2xy^2)^3 \times (4x^3y)^2}{4^2x^{10}y^2 \times 2x^4y^4}$ .

Simplify the terms in the numerator using the exponent rules $(ab)^n = a^nb^n$ and $(x^a)^b = x^{ab}$ .
$(2xy^2)^3 = 2^3x^3(y^2)^3 = 8x^3y^6$ $(4x^3y)^2 = 4^2(x^3)^2y^2 = 16x^6y^2$
Now, multiply these simplified terms together:
$8x^3y^6 \times 16x^6y^2 = (8 \times 16)x^{3+6}y^{6+2} = 128x^9y^8$
Simplify the terms in the denominator.
$4^2x^{10}y^2 \times 2x^4y^4 = 16x^{10}y^2 \times 2x^4y^4$
Multiply these terms together:
$(16 \times 2)x^{10+4}y^{2+4} = 32x^{14}y^6$
Divide the simplified numerator by the simplified denominator using the exponent rule $\frac{x^a}{x^b} = x^{a-b}$ .
$\frac{128x^9y^8}{32x^{14}y^6}$
Divide the numerical coefficients:
$\frac{128}{32} = 4$
Divide the $x$ terms:
$\frac{x^9}{x^{14}} = x^{9-14} = x^{-5}$
Divide the $y$ terms:
$\frac{y^8}{y^6} = y^{8-6} = y^2$
Combine the simplified terms and express with positive exponents.
$4x^{-5}y^2 = \frac{4y^2}{x^5}$
The simplified expression is $\mathbf{\frac{4y^2}{x^5}}$ .

Answer