Question

Simplify.
Rewrite the expression in the form b^n

(b^3)^2

Answer 1

Explanation:

`a^n={\underbrace{a\cdot a\cdot a\cdot...\cdot a}_(n)`

METHOD 1.

`\left(b^3\right)^2=\underbrace{b^3\cdot b^3}_(2)=\underbrace{b\cdot b\cdot b}_(3)\cdot\underbrace{b\cdot b\cdot b}_(3)=\underbrace{b\cdot b\cdot b\cdot b\cdot b\cdot b}_(6)=b^6`

METHOD 2.

`\left(b^3\right)^2=\underbrace{b^3\cdot b^3}_(2)=b^(3+3)=b^6\qquad\text{used}\ a^n\cdot a^m=a^(n+m)`

METHOD 3.

`\left(b^3\right)^2=\left(\underbrace{b\cdot b\cdot b}_(3)\right)^2=b^2\cdot b^2\cdot b^2=b^(2+2+2)=b^6\\\text{used}\ (ab)^n=a^nb^n,\ a^n\cdot a^m=a^(n+m)`

METHOD 4.

`\left(b^3\right)^2=b^(3\cdot2)=b^6\qquad\text{used}\ \left(a^n\right)^m=a^(nm)`