Product and Quotient Rules
Simplify a2 x a5
a7
2 + 5 = 7
What is 6a0
6
6 x 1 = 6
Simplify (y4)2
y8
4 x 2 = 8
Simplify (2 x 5)4
24 x 54 or 10 000
A value is cubed then squared. Write an expression for this and simplify.
(a3)2
Simplify y8/y5
y3
8 - 5 = 3
Simplify (43 x 70)
43
43 x 1 = 43
If (ma)3 = m18, what is a?
6
3 x 6 = 18
Simplify (2/3)2
22/32 or 4/9
Simplify (x2y)3
x6y3
Simplify (2a6 x 3b4)/(4a2 x 9b)
(a4 x b3)/6
Had to use normal division, product rule, and quotient rule.
True or False
00 = 1
False
It does not exist or is undefined
Simplify ((22)4)6
248
2 x 4 x 6 = 48
Simplify (a3b2/c)2
a6b4/c2
A number multiplies by itself 9 times, then divides by itself 4 times. Write an expression and simplify.
a5
a9/a4
Multiply a number by itself 6 times, then divide by itself 4 times. Write an equation for this, then simplify.
a2
a6/a4 = a2
Simplify (a0b3c0)4
b12
1 x b12 x 1
Simplify ((23a2y4)2 x (4a3y)3)2
412a26y22
Will accept 21246a26y22
Had to use the power rule on both the inside brackets. Then use the power the rule on the outside brackets. Then finish with the product rule.
Simplify (3ay/4z)3
27a3y3/64z3
A rabbit enclosure has 24 rabbits. The number doubles 3 times and then halves once. How many rabbits are in the enclosure now?
64 or 26
24 x 23/2 = 26
Bacteria triples every hour. It starts at 32 cells. How many cells will there be after 5 hours
37 or 2187
32 x 35 = 37
It triples every hour, for 5 hours, so the starting value must be multiplied by 3, five times. I.e. 35
Halve a number, multiply the result by 0.25, raise the result to the power of 0. What number are you left with?
1
Anything (besides 0) raised to the power of 0 equals 1
A pattern doubles at each stage for the first 4 stages, and is then cubed at each stage after that. The pattern starts with 5 objects. How many objects will their be after the fifth stage?
(5 x 24)3 or (80)3 or 512 000
Doubling for 4 stages gives us 24. This must be multiplied by the original amount to find the number after 4 stages. The total after 4 stages is then cubed at the fifth stage.
Code A=2, B=3, C=5
Simplify (A3BC2/B2)2
40 000/9
Had to simplify to A6C4/B2, then substitute the code numbers in.
A special vault has a security mechanism involving layers of code numbers.
Every time a new layer is added, the existing code numbers is multiplied by 5.
After every third layer, the entire number is raised to the power of 4.
The initial code numbers is 52. What will the code number be after 6 layers have been added?
592
Needed to add 1 to the power at each additional layer. At the third and sixth layers, needed to add 1 to the power and then multiply it by 4.