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12345 [234]
2 years ago
9

Which expression is equivalent to (x^6y^8)^3\x^2y^2

Mathematics
2 answers:
BARSIC [14]2 years ago
8 0

Answer: x^{16}\ y^{22}

Step-by-step explanation:

The given expression : \dfrac{(x^6y^8)^3}{x^2y^2}

Using identity , (a^m)^n=a^{mn} , we have

{(x^6y^8)^3=x^{6\times3}\ y^{8\times3}\\\\=x^{18}\ y^{24}

Now, \dfrac{(x^6y^8)^3}{x^2y^2}=\dfrac{x^{18}\ y^{24}}{x^2\ y^2}

( its also an equivalent expression to given expression.)

Using identity , \dfrac{a^n}{a^m}=a^{n-m} , we have

\dfrac{x^{18}\ y^{24}}{x^2\ y^2}=x^{18-2}\ y^{24-2}\\\\=x^{16}\ y^{22}

Hence, the expression is equivalent to given expression :

x^{16}\ y^{22}

Damm [24]2 years ago
5 0

Answer:

\large\boxed{\dfrac{(x^6y^8)^3}{x^2y^2}=x^{16}y^{22}}

Step-by-step explanation:

\dfrac{(x^6y^8)^3}{x^2y^2}\qquad\text{use}\ (ab)^n=a^nb^n\ \text{and}\ (a^n)^m=a^{nm}\\\\=\dfrac{(x^6)^3(y^8)^3}{x^2y^2}=\dfrac{x^{(6)(3)}y^{(8)(3)}}{x^2y^2}=\dfrac{x^{18}y^{24}}{x^2y^2}\qquad\text{use}\ \dfrac{a^m}{a^n}=a^{m-n}\\\\=x^{18-2}y^{24-2}=x^{16}y^{22}

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