Complete the tables and explain the general rule for multiplying and dividing exponents with the same base.

Here are the solutions to your questions.

ACTIVITY 1: MULTIPLICATION OF EXPONENTS

1.1.1 Complete the following table by using your calculator. The first line has been done for you as an example.

$a^m$	$a^n$	$a^m \times a^n$	Prime Factors	$a^{m+n}$
$2^2$	$2^3$	32	$2^5$	$2^{2+3} = 2^5$
$3^3$	$3^3$	729	$3^6$	$3^{3+3} = 3^6$
$2^4$	$2^4$	256	$2^8$	$2^{4+4} = 2^8$
$3^5$	$3^2$	2187	$3^7$	$3^{5+2} = 3^7$
$5^3$	$5^7$	9765625	$5^{10}$	$5^{3+7} = 5^{10}$
$a^3$	$a^4$	$a^7$	$a^7$	$a^{3+4} = a^7$
$2^x$	$2^y$	$2^{x+y}$	$2^{x+y}$	$2^{x+y}$

1.1.2 Explain the general rule of what is happening in the table above in your own words.
When multiplying powers that have the same base, you add their exponents together and keep the base unchanged.

1.1.3 Complete the rule in symbols:
$a^m \times a^n = a^{\boxed{m+n}}$

ACTIVITY 2: DIVISION OF EXPONENTS

1.2.1 Complete the following table by using your calculator. The first line has been done for you as an example.

$a^m$	$a^n$	$a^m \div a^n$	Prime Factors	$a^{m-n}$
$2^5$	$2^3$	4	$2^2$	$2^{5-3} = 2^2$
$3^3$	$3^3$	1	$3^0$	$3^{3-3} = 3^0$
$2^6$	$2^5$	2	$2^1$	$2^{6-5} = 2^1$
$3^{14}$	$3^5$	19683	$3^9$	$3^{14-5} = 3^9$
$5^7$	$5^3$	625	$5^4$	$5^{7-3} = 5^4$
$a^6$	$a^4$	$a^2$	$a^2$	$a^{6-4} = a^2$
$2^x$	$2^y$	$2^{x-y}$	$2^{x-y}$	$2^{x-y}$

1.2.2 Explain the general rule of what is happening in the table above in your own words.
When dividing powers that have the same base, you subtract the exponent of the divisor from the exponent of the dividend, keeping the base the same.

1.2.3 Complete the rule in symbols:
$a^m \div a^n = a^{\boxed{m-n}}$