how do you get the answer?

Question

(x³y⁶)³

Answer 1

Hey Lizzy -- for small 'powers', we can just "spell it out" if we're unsure ...

 

[xxx yyy yyy] [xxx yyy yyy] [xxx yyy yyy] = x^9 y^18 ... All the best :)

Answer 2

I like Brad's analysis and Vivian's use of the Power Rule of Exponents.

 

I showed my classroom students these examples for the Rules of Exponents [* means multiply]:

 

(3^2) * (3^3) = (3*3)*(3*3*3) = 3^5 = 3^(2+3) ==> a^m * a^n = a^(m+n)

 

(3^3)/(3^2) = (3*3*3)/(3*3*1) = 3/1 = 3 = 3^(3-2) ==> a^m / a^n = a^(m-n)

 

(3^2)/(3^3) = (3*3*1)/(3*3*3) = 1/3 = 3^(2-3) = 3^(-1) ==> a^(-m) = 1/(a^m)

 

(3^2)/(3^2) = (3*3)/(3*3) = 1 = 3^(2-2) = 3^0 ==> a^0 = a/a = 1 only if a ≠ 0

 

(3^2)^3 = (3*3)*(3*3)*(3*3) = 3^6 = 3^(2*3) ==> (a^m)^n = a^(mn)

 

If you understand the examples above, you should never fear forgetting the rules.

Answer 3

Hi Lizzy;

(x³y⁶)³

x⁹y¹⁸

This is because the exponentials must be multiplied together...

(3)(3)=9

(6)(3)=18