We read your photo as:

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

Mathematics

ScanSolve AI Answer

Answers

2 parts
2.3

b13\mathbf{b^{13}}

2.4

4y2x5\mathbf{\frac{4y^2}{x^5}}

Step-by-step solution

7 steps

You got it, merro! Let's finish these problems.

Part 2

(continued)

Part 2.3

b13\mathbf{b^{13}}

Simplify a2b3(a3b)2(a−2b2)−4\frac{a^2b^3(a^3b)^2}{(a^{-2}b^2)^{-4}}.

  1. Simplify the numerator using exponent rules (xy)n=xnyn(xy)^n = x^ny^n and xaxb=xa+bx^a x^b = x^{a+b}.

    a2b3(a3b)2=a2b3(a3×2b1×2)=a2b3(a6b2)=a2+6b3+2=a8b5a^2b^3(a^3b)^2 = a^2b^3(a^{3 \times 2}b^{1 \times 2}) = a^2b^3(a^6b^2) = a^{2+6}b^{3+2} = a^8b^5

  2. Simplify the denominator using exponent rules (xy)n=xnyn(xy)^n = x^ny^n and (xa)b=xab(x^a)^b = x^{ab}.

    (a−2b2)−4=a(−2)×(−4)b2×(−4)=a8b−8(a^{-2}b^2)^{-4} = a^{(-2) \times (-4)}b^{2 \times (-4)} = a^8b^{-8}

  3. Divide the simplified numerator by the simplified denominator using the rule xaxb=xa−b\frac{x^a}{x^b} = x^{a-b}.

    a8b5a8b−8=a8−8b5−(−8)=a0b5+8=1⋅b13=b13\frac{a^8b^5}{a^8b^{-8}} = a^{8-8}b^{5-(-8)} = a^0b^{5+8} = 1 \cdot b^{13} = b^{13}

    The simplified expression is b13\boxed{\mathbf{b^{13}}}.

Part 2.4

4y2x5\mathbf{\frac{4y^2}{x^5}}

Simplify (2xy2)3×(4x3y)242x10y2×2x4y4\frac{(2xy^2)^3 \times (4x^3y)^2}{4^2x^{10}y^2 \times 2x^4y^4}.

  1. Simplify the terms in the numerator.

    (2xy2)3=23x3(y2)3=8x3y6(2xy^2)^3 = 2^3x^3(y^2)^3 = 8x^3y^6 (4x3y)2=42(x3)2y2=16x6y2(4x^3y)^2 = 4^2(x^3)^2y^2 = 16x^6y^2

    Multiply these simplified terms:

    8x3y6×16x6y2=(8×16)x3+6y6+2=128x9y88x^3y^6 \times 16x^6y^2 = (8 \times 16)x^{3+6}y^{6+2} = 128x^9y^8

  2. Simplify the terms in the denominator.

    42x10y2×2x4y4=16x10y2×2x4y44^2x^{10}y^2 \times 2x^4y^4 = 16x^{10}y^2 \times 2x^4y^4

    Multiply these terms:

    (16×2)x10+4y2+4=32x14y6(16 \times 2)x^{10+4}y^{2+4} = 32x^{14}y^6

  3. Divide the simplified numerator by the simplified denominator.

    128x9y832x14y6\frac{128x^9y^8}{32x^{14}y^6}

    Divide the numerical coefficients:

    12832=4\frac{128}{32} = 4

    Divide the xx terms:

    x9x14=x9−14=x−5\frac{x^9}{x^{14}} = x^{9-14} = x^{-5}

    Divide the yy terms:

    y8y6=y8−6=y2\frac{y^8}{y^6} = y^{8-6} = y^2

  4. Combine the simplified terms.

    4x−5y2=4y2x54x^{-5}y^2 = \frac{4y^2}{x^5}

    The simplified expression is 4y2x5\boxed{\mathbf{\frac{4y^2}{x^5}}}.

Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question

More Mathematics Questions

QSimplify the expression: 2(x)² × (1/4)xy * 8x / ((3x × 4y)⁻¹)⁻²QSimplify the following expression: (36x2 - 9y2) / 4xy - 20xy / (6x − 3y)QSimplify the expression: y = (3x3 + 4x4 + 2x2) / xQSimplify: (3x2 - 9y2)/(xy) × (20xy)/(6x − 3y)
Browse by topic:Algebra
See all Mathematics questions →
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp