Complete the following exercises on exponents and powers: 2.3 Complete the rule in symbols: a^m / aⁿ = a^? (a^m)ⁿ = a^? 3 Complete the following table using your calculator (first line is an example

here are the solutions to the math questions.

1.2.3 Complete the rule in symbols:

• $a^m \div a^n = a^{\boxed{m-n}}$
• $(a^m)^n = a^{\boxed{m \times n}}$

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

$a^m$	$a^n$	$(a^m)^n$	Prime Factors	$a^{m \times n}$
$2^2$	3	$(2^2)^3$	$64 = 2^6$	$2^{2 \times 3} = 2^6$
$3^2$	4	$(3^2)^4$	$3^8$	$3^{2 \times 4} = 3^8$
$3^3$	2	$(3^3)^2$	$3^6$	$3^{3 \times 2} = 3^6$
$2^4$	5	$(2^4)^5$	$2^{20}$	$2^{4 \times 5} = 2^{20}$
$5^3$	2	$(5^3)^2$	$5^6$	$5^{3 \times 2} = 5^6$
$a^2$	$x$	$(a^2)^x$	$a^{2x}$	$a^{2 \times x} = a^{2x}$
$2^x$	$y$	$(2^x)^y$	$2^{xy}$	$2^{x \times y} = 2^{xy}$

1.3.2 Explain the general rule of what is happening in the table above in your own words.
When a power is raised to another power, the exponents are multiplied together, while the base remains the same.

1.3.3 Complete the rule in symbols:
$(a^m)^n = a^{\boxed{mn}}$

1.3.4 Does this rule apply for every number in the bracket? $(2 \times 3)^2 \times (3 \times 2)^2$? Show your workings.
Yes, the rule $(a^m)^n = a^{mn}$ applies to each factor within the bracket.