Question

multiplying and dividing monomials - item 7632
question 6
what is a correct way to rewrite ( a^b a^c )?
options:
( a^{(b + c)} )
( a^2 bc )
( 2a^{(b + c)} )
( a^{bc} )

Explanation:

Step1: Recall exponent rule for multiplication

When multiplying two powers with the same base, we add the exponents: $x^m \cdot x^n = x^{m + n}$. Here, the base is $a$, and the exponents are $b$ and $c$.

Step2: Apply the rule to $a^b \cdot a^c$

Using the rule $x^m \cdot x^n = x^{m + n}$, substitute $x = a$, $m = b$, and $n = c$. So, $a^b \cdot a^c = a^{b + c}$.

Answer:

$\boldsymbol{a^{(b + c)}}$ (corresponding to the option with $a^{(b + c)}$)