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Question 1

When I see a lot of decimals…

Answer 1

I will get rid of decimals in the denominator, make the adjustments by the same number of places in the numerator, then simplify

Question 2

Answer 2

I think…

1) Get to the same base
2) Continue to simplify (in this case, multiple the nesting #s)
3) Once the base is the same (exponents gone), remove the base

Question 3

When I see … (4^w)³ = 32^w-1

Answer 3

When I see exponents on both sides

I think to get to either get to the same base or the same exponents and simplify

(4^w)³ = 32^w-1

–> ((2²)^w)³ = (2⁵)^w-1

–> 2^6w = 2^5w-5

–>6w = 5w-5

–> w = -5

Question 4

When I see a lot of fractions and simple answer choices…

Answer 4

I think …

WORK BACKWARDS and plug in answer choices!

Question 5

Answer 5

1) For 4.8, find a close number that has an easy square root. In this case it’s 49
2) Since the decimal needs to be moved, make sure the power is changed to a lower power since the number is getting bigger
3) When you are multiplying by a square root, you can break up the square to simplify
4) 10⁸ can be simplified to (10⁴)², then you can take square root. When you see that you need to root an exponent, you need to follow similar rules to regular numbers, so try and simplify to a power of 2 to drop the root

Question 6

When I see an increased ratio by a certain number and it creates a new ratio

Answer 6

I will turn it into an equation where the initial ratio has 1 unknown and you are just adding the numbers to that fraction. Then on the other side, you just list out the new ratio (with no unknowns) and solve for unknown

Question 7

When I see in the question “all possible values”…

Answer 7

I know that there are 2 potential solutions to the problem.

In this case, because I see an absolute value, I know that between the absolute value it could be positive or negative.

Question 8

When I see 2 square roots with 2 unknowns..

Answer 8

I can put the square root on each side of the equal sign and that cancels out the square root

Question 9

When I see that I need to take the square root of an unknown…

Answer 9

I know there are 2 possible answer choices because X can be positive or negative. If you ever have to square an unknown yourself, you don’t know if it’s positive or negative.

Question 10

When I see a problem where they are adding to a ratio…

Solve problem :)

Answer 10

I will turn in to an equation and add X to both parts of the ratio, solve for X, then plug back in