Math help please? =) Algebra.?

Question

Could someone solve and explain with steps these two problems I am having difficulty with? =) Thanks.

1.) (5x^5)^3(1/25x^5)^2

2.) (5u^2 v^5)^5(5u^5 v)^-2

Thanks again.

Answer 1

In the first, simplify 1/25 into 5^-2. Then use the order of operations (PEMDAS) and exponent rules.

(5x^5)^3) is 5^3*x^(5*3) = 125x^15
(1/25x^5)^2) is 5^-4x^10
5^3*5^-4=5^(3-4)=5^-1= 1/5
x^15*x^10 = x^(15+10)=x^25

Answer: 1/5 x^25

Do the second the same way.

Answer 2

Remember the rule

x^m * x^n = x^(m+n) x^m/x^n = x^(m-n) and (x^m)^n = x^(mn)

5^3 * x^15 / (5^4) * x^10 (I am not sure if X^5 is in the demo)
= 1/5 * x^25 (if X^5 is part of the num)
or 1/5 x x^5 (if x^5 is part the demo)

(5^5 * u^10 * v^25) * (5^-2 * u^-10 * v^-2)
5^(5-2) * u^(10-10) * v^(25-2)
5^3 * u^0 * v^(23)
125v^23 (u^0 = 1)

Answer 3

1.) (5x^5)^3(1/25x^5)^2
(5x^5)^3 = 5^3*x^15
(1/25x^5)^2 = 1/5^4*x^10
So together, it's (x^25)/5

2.) (5u^2 v^5)^5(5u^5 v)^-2
(5u^2v^5)^5 = 5^5u^10v^25
(5u^5v)^-2 = 1 / (5^2u^10v^2)
So together, it's 5^3v^23 (u's cancel)

Answer 4

tip: PEMDAS. you may already know this, but if not, this helps alot! Here ya go:
P parenthesis
E exponets
M multiplication or
D division
A addition or
S subtraction


do these certain steps in this order! good luck!