Simplify 3x²(2xy - 3xy² + 4x²y³)

Simplified value of 3x²(2xy - 3xy² + 4x²y³) is x³y − 9x³y² + 12x⁴y³ the detailed solution for the same is added below:

Simplify 3x²(2xy - 3xy² + 4x²y³)

Solution:

Given,

• 3x²(2xy − 3xy² + 4x²y³)

Using distributive property and law of exponent {a^m. aⁿ = a^m+n}

We have:

= 6x²⁺¹y − 9x²⁺¹y² + 12x²⁺²y³

= 6x³y − 9x³y² + 12x⁴y³

Also Read:

• Negative Exponents
• How to multiply and divide exponents
• Adding and Subtracting of Exponents
• Laws of Exponents for Real Numbers

Similar Questions

Question 1. Simplify: \frac{4ab^2(-5ab^3)}{10a^2b^2} .

Solution:

Multiply the terms in the numerator, using the multiplication law of exponents.

\frac{4ab^2(-5ab^3)}{10a^2b^2} = \frac{-20(a)^{1+1}(b)^{2+3}}{10a^2b^2}

= \frac{-2a^2b^5}{a^2b^2}

Now apply the division law of exponents to evaluate.

= -2a^2-2b^5-2

= -2a⁰b³

= -2b³

Question 2. Simplify: \dfrac{(p^{1/7})^{49}}{\left(\dfrac{14p^{1/2}}{(p^{26})^{-1/7}}\right)}

Solution:

Using the property (p^m)ⁿ = p^mn, we have:

\dfrac{(p^{1/7})^{49}}{\left(\dfrac{14p^{1/2}}{(p^{26})^{-1/7}}\right)}=\dfrac{p^{49/7}}{\left(\dfrac{14p^{1/2}}{p^{-26/7}}\right)}

Apply the property a^m/aⁿ = a^m-n in the denominator.

= \dfrac{p^7}{{14p^{1/2-(-26/7)}}}

= \dfrac{p^7}{{14p^{59/14}}}

Again applying the quotient law of exponents, we have:

= \frac{{p^{7-\frac{59}{14}}}}{14}

= \frac{p^{\frac{39}{14}}}{14}

Question 3. Simplify: [25 × t^-4]/[5^-3 × 10 × t^-8].

Solution:

[25 x t^-4]/[5^-3 x 10 x t^-8] = (5² × t⁻⁴)/(5⁻³ × 5 × 2 × t⁻⁸ )

= (52 × t⁻⁴)/(5⁻³⁺¹ × 2 × t⁻⁸)                           [Since, am × an = am+n]

= (5² × t⁻⁴)/(5⁻² × 2 × t⁻⁸)

= (5²⁻⁽⁻²⁾ × t^{−4−(−8)})/2                                       [Since, am/an = am−n]

= (5⁴ × t^{−4 + 8})/2

= (625/2)(t⁴)

Question 4. Simplify: 3x²/10x⁵.

Solution:

Using the property a^m/ aⁿ = a^m-n, which is known as the quotient law,

3x²/10x⁵ = \frac{3x^{2-5}}{10}

= 3x^-3/ 10

Using the property a^-m = 1/ a^m, which is known as the Negative exponent law,

3x^-3/ 10 = \frac{3}{10x^{3}}

Question 5. Simplify: 12x⁹/5x⁶⁰.

Solution:

Using the property a^m/ aⁿ = a^{m - n}, which is known as the quotient law,

12x⁹/ 5x⁶⁰ = \frac{12x^{9-60}}{5}

= 12x^-51/ 5

Using the property a^-m = 1/a^m, which is known as the Negative exponent law,

12x^-51/ 5 = \frac{12}{5x^{51}}.