Question

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

Answer 1

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 :

$x^{16}\ y^{22}$

Answer 2

Answer:

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

Step-by-step explanation:

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