Question

1. simplify (hint: product rule of exponents) $x^2 \cdot x^7$

Explanation:

Step1: Recall product rule of exponents

The product rule of exponents states that for any real number \( x \) and integers \( m \) and \( n \), \( x^m \cdot x^n = x^{m + n} \).

Step2: Apply the product rule

Here, \( m = 2 \) and \( n = 7 \), so we add the exponents: \( x^2 \cdot x^7 = x^{2 + 7} \).

Step3: Simplify the exponent

Calculate \( 2 + 7 = 9 \), so \( x^{2 + 7} = x^9 \).

Answer:

\( x^9 \)