Question

what expression is equivalent to $x^5 \cdot x^7$?
\bigcirc $x^{\frac{5}{7}}$
\bigcirc $x^2$
\bigcirc $x^{12}$
\bigcirc $x^{35}$

Explanation:

Step1: Recall exponent rule for multiplication

When multiplying two exponential expressions with the same base, we use the rule \( a^m \cdot a^n = a^{m + n} \). Here, the base is \( x \), \( m = 5 \) and \( n = 7 \).

Step2: Apply the rule

Calculate the sum of the exponents: \( 5+7 = 12 \). So \( x^5\cdot x^7=x^{5 + 7}=x^{12} \).

Answer:

C. \( x^{12} \) (assuming the third option is labeled C, if the options are labeled as per the order: first option \( x^{\frac{5}{7}} \), second \( x^2 \), third \( x^{12} \), fourth \( x^{35} \))