a] 4¹×4²
From the laws of integer when you multiply number with the same base, you add their powers. Thus we shall have:
4¹×4²
=4⁽¹⁺²⁾
=4³
=64
Answer: 64
Answer: 64
b. 5³×5⁻⁶
since the numbers have the base, we add their powers:
5³×5⁻⁶
=5⁽³⁻⁶⁾
=5⁻³
according to the integer laws
a⁻ᵇ=1/aᵇ
thus our expression will be:
5⁻³
=1/5³
=1/125
Answer: 1/125
c. 3²×3¹
=3⁽²⁺¹⁾
=3³
=9
Answer: 9
d.
6⁵×5⁻⁷
=6⁵/5⁷
=7776/78125
Answer: 7776/78125
e.
8⁵/8³
when you divide numbers with the same base you subtract their powers as follows:
8⁵/8³
=8⁽⁵⁻³⁾
=8²
=64
Answer: 64
f. 7²/7⁴
As in the above question we shall have:
7²/7⁴
=7⁽²⁻⁴⁾
=7⁻²
=1/7²
=1/49
Answer: 1/49
g.
9⁵/9⁷
=9⁽⁵⁻⁷⁾
=9⁻²
=1/9²
=1/81
Answer: 1/81
h.
5¹/5³
=5⁽¹⁻³⁾
=5⁻²
=1/5²
=1/25
Answer: 1/25
Select two of the above
expressions (one multiplication and one division) and explain how you
simplified them.
a] 4¹×4²
From the laws of integer when you multiply number with the same base, you add their powers. Thus we shall have:
4¹×4²
=4⁽¹⁺²⁾
=4³
=64
b]
8⁵/8³
when you divide numbers with the same base you subtract their powers as follows:
8⁵/8³
=8⁽⁵⁻³⁾
=8²
=64
