Simplifying powers with the same base

Text

Simplify, leaving the result as a power:

• (a) $a^{9}\cdot a^{4}$
• (b) $12\,b^{7}\div 3\,b^{2}$
• (c) $\left(3c^{4}\right)^{3}$
• (d) $\dfrac{m^{5}\cdot m}{m^{2}}$

Solution

(a) Add the exponents: $a^{9+4}=a^{13}$. (b) $\dfrac{12}{3}\,b^{7-2}=4b^{5}$. (c) Raise both coefficient and exponent: $3^{3}c^{4\cdot 3}=27c^{12}$. (d) $\dfrac{m^{6}}{m^{2}}=m^{4}$.

$\boxed{\;(a)\;a^{13}\qquad (b)\;4b^{5}\qquad (c)\;27c^{12}\qquad (d)\;m^{4}\;}$