Question

what is the relationship between ( x^4 \times x^6 ) and ( x^{10} )?

• they are not equal
• they are equal because ( 4 \times 6 = 24 )
• they are equal by coincidence
• they are equal because ( 4 + 6 = 10 )

Explanation:

Step1: Recall exponent rule for multiplication

When multiplying exponential terms with the same base, we use the rule \(a^m \times a^n=a^{m + n}\). For the base \(x\), \(x^4\times x^6\) follows this rule.

Step2: Apply the exponent rule

Using \(a^m\times a^n=a^{m + n}\) where \(a = x\), \(m = 4\) and \(n=6\), we get \(x^4\times x^6=x^{4 + 6}\).

Step3: Simplify the exponent

Calculate \(4+6 = 10\), so \(x^4\times x^6=x^{10}\). So they are equal because when multiplying exponents with the same base, we add the exponents (\(4 + 6=10\)).

Answer:

They are equal because \(4 + 6 = 10\) (the option with this explanation)