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Can anyone help? 80 points!

Can anyone help? 80 points!-example-1

2 Answers

12 votes

Answer:


4x^2y^3\sqrt[3]{x^2y}

Explanation:

Given expression:


\left(8x^4y^5\right)^{(2)/(3)}

Rewrite 4 as (3 + 1) and 5 as (3 + 2):


\implies \left(8x^((3+1))y^((3+2))\right)^{(2)/(3)}


\textsf{Apply exponent rule} \quad a^(b+c)=a^b \cdot a^c:


\implies \left(8x^3xy^3y^2}\right)^{(2)/(3)}


\textsf{Apply exponent rule} \quad (a^b)^c=a^(bc):


\implies 8^{\left((2)/(3)\right)}x^{\left(3 *(2)/(3)\right)}x^{\left((2)/(3)\right)}y^{\left(3 * (2)/(3)\right)}y^{\left(2 * (2)/(3)\right)}}


\implies 4x^2x^{(2)/(3)}y^2y^{(4)/(3)}


\implies 4x^2y^2x^{(2)/(3)}y^{(4)/(3)}

Rewrite 4/3 as 1 + 1/3:


\implies 4x^2y^2x^{(2)/(3)}y^{\left(1+(1)/(3)\right)}


\textsf{Apply exponent rule} \quad a^(b+c)=a^b \cdot a^c:


\implies 4x^2y^2x^{(2)/(3)}y^1y^{(1)/(3)}


\implies 4x^2y^2y^1x^{(2)/(3)}y^{(1)/(3)}


\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^(b+c)


\implies 4x^2y^((2+1))x^{(2)/(3)}y^{(1)/(3)}


\implies 4x^2y^3x^{(2)/(3)}y^{(1)/(3)}


\textsf{Apply exponent rule} \quad a^(bc)=(a^b)^c:


\implies 4x^2y^3\left(x^2\right)^{(1)/(3)}y^{(1)/(3)


\textsf{Apply exponent rule} \quad a^b \cdot c^b=ac^b:


\implies 4x^2y^3\left(x^2y\right)^{(1)/(3)


\textsf{Apply exponent rule} \quad a^{(1)/(n)}=\sqrt[n]{a}:


\implies 4x^2y^3\sqrt[3]{x^2y}

User Jamie Hale
by
7.7k points
3 votes

Answer:

  • D)
    4x^2y^3\sqrt[3]{x^2y}

Explanation:

Given expression:


  • (8x^4y^5)^{(2)/(3)

Simplify in steps, using below properties of exponents:


  • a^ba^c= a^(b+c) Product of Powers Property

  • (a^b)^c=a^(bc) Power of Power Property

Solution:


  • (8x^4y^5)^{(2)/(3) =

  • (2^3x^4y^5)^{(2)/(3) =

  • 2^{(3*2)/(3)} x^{(4*2)/(3)} y^{(5*2)/(3)} =

  • 2^2x^{(8)/(3)}y^{(10)/(3) =

  • 4x^{2(2)/(3)}y^{3{(1)/(3) =

  • 4x^2x^{(2)/(3)} y^3y^{(1)/(3)} =

  • 4x^2y^3(x^2y)^{(1)/(3)}=

  • 4x^2y^3\sqrt[3]{x^2y}

Correct choice is D

User Yunandtidus
by
6.6k points