Question

1. write two equivalent expressions for 4^6 ÷ 4^3, one with exponents and one without exponents.

Explanation:

Step1: Use exponent - division rule

According to the rule $a^m\div a^n=a^{m - n}$, for $4^6\div4^3$, we have $4^{6 - 3}=4^3$.

Step2: Expand without exponents

$4^6=4\times4\times4\times4\times4\times4$, $4^3=4\times4\times4$. Then $4^6\div4^3=\frac{4\times4\times4\times4\times4\times4}{4\times4\times4}=4\times4\times4 = 64$.

Answer:

With exponents: $4^3$; Without exponents: $64$