Question

simplify to a single power of 4: \\(dfrac{4^{7}}{4^{6}}\\) answer attempt 1 out of 2 answer: \\(4^{square}\\) submit answer

Explanation:

Step1: Recall exponent rule for division

When dividing exponents with the same base, we use the rule \( \frac{a^m}{a^n} = a^{m - n} \). Here, the base \( a = 4 \), \( m = 7 \), and \( n = 6 \).

Step2: Apply the exponent rule

Substitute the values into the rule: \( \frac{4^7}{4^6} = 4^{7 - 6} \)

Step3: Simplify the exponent

Calculate \( 7 - 6 = 1 \), so \( 4^{7 - 6} = 4^1 \)

Answer:

\( 4^1 \) (or just \( 4 \), but since the form is \( 4^{\square} \), the exponent is 1)