Question

Simplify. Rewrite the expression in the form b^n (b^3)^2

Answer 1

Step-by-step 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.

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