math-algebra

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How do i solve these problems:

1. 2(-5y^3)^2+(-3y^3)^3

2. Lemon juice is 10^2 times as acidic as tomato juice. Tomato juice is 10^3 times as acidic as egg whites. How many times as acidic is lemon juice as egg whites? Write as a monomial.

3. The seismic waves of a magnitude 6 earthquake are 10^2 times as great as a magnitude 4 earthquake. The seismic waves of a magnitude 4 earthquake are 10 times as great as a magnitude 3 earthquake. How many times as great are the seismic waves of a magnitude 6 earthquake as those of a magnitude 3 earthquake? Write a monomial.

• math-algebra -

These problems are all very similar and you have not tried them so I will do the third and you try the others

call magnitude 3 = q for quake
then mag 4 = 10^1 q
then mag 6 = 10^2 *10^1 q = 10^3 q = 1000 times the mag 3

M6 = 10^3 M3

in general by the way
Msub(n+1) = 10 Msub(n)

• math-algebra -

In number 2
10^2*10^3 = 10^(2+3) = 10^5

to multiply, add exponents of same quantity
to raise to power, multiply exponents
remember:
x^2* x^3 = x^(2+3) = x^5
BUT
(x^2)^3 = x^(2*3) = x^6

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