Question

(a^3 )^3(x^5 )^2(y^2 )^5(c^3 )^4​

Answer 1

$\boxed{(a^m)^n=a^{mn}}\\\\(a^3)^3=a^{3*3}=\boxed{\bf a^9}\\\\(x^5 )^2=x^{5*2}=\boxed{\bf x^{10}}\\\\(y^2 )^5=y^{2*5}=\boxed{\bf y^{10}}\\\\(c^3 )^4=c^{3*4}=\boxed{\bf c^{12}}$

Answer 2

To simplify the expression $(a^3)^3(x^5)^2(y^2)^5(c^3)^4$, you can apply the properties of exponents. When you raise an exponentiated expression to another exponent, you multiply the exponents. So:

$(a^3)^3 = a^{3*3} = a^9$

$(x^5)^2 = x^{5*2} = x^{10}$

$(y^2)^5 = y^{2*5} = y^{10}$

$(c^3)^4 = c^{3*4} = c^{12}$

Now, you can combine these results to simplify the entire expression:

$a^9 * x^{10} * y^{10} * c^{12}$

So, the simplified expression is $a^9x^{10}y^{10}c^{12}$.