Product
y3 x y5
y8
x8 / x3
x5
(x4)2
x8
(ab)3
a3b3
Without calculating the full value:
75 x 7-5
Explain why the answer must be 1.
Using the rule am x an = am+n
75 x 7-5 = 70
And anything to the power of zero equals 1.
So the answer must be 1.
a7 x a-2
a5
a4/ a7
a-3
(a3)5
a15
(2x)4
16x4
A student writes:
x3 + x2 = x5
Are they correct? Explain
No.
You only add powers when multiplying powers with the same base.
3m4 x 2m3
6m7
15m6/ 3m2
(m-2)4
m-8
(x/y)3
x3 / y3
Find the mistake
(x4)2 = x6
Explain what law should have been used.
Mistake - used the Product Law
Correct Law - Power of a Power
z-5 x z8
z3
x-2/x5
x-7
((x2)3)2
x12
(3a2b)2
9a4b2
Without expanding, determine which is larger:
210 or 45
Justify your answer.
Equal.
If you re-write 45 with a base of 2, you get (22)5, which is equal to 210
(2a3b2) x (5a-4b5)
10a-1b7
12a7b3 / 4a2b5
3a5b-2
((a-3)2)4
a-24
(2x2y / 3z)3
8x6y3 / 27z3
A student claims:
(a2b3)2 = a4b5
Explain why this is incorrect and give the correct answer
Incorrect because they have used the Product Rule, not the Power of a Power for the exponent of b.
Correct Answer - a4b6