2 algebra questions?

Question

Simplify M^2/3 divided by M^1/5

The square root of (2x+4) +1 is greater than or equal to 5
****square root bar is only over 2x+4****

Answer 1

PROBLEM 1:

Are the fractions the exponents? I assume so...

M^(2/3) / M^(1/5)

Here the rule is if you are dividing numbers with the same bases, you subtract the exponents:
= M^(2/3 - 1/5)

The common denominator is 15, so multiply the first fraction by 5 (top and bottom) and the second fraction by 3 (top and bottom):
= M^(10/15 - 3/15)

Now subtract:
= M^(7/15)

PROBLEM 2:

sqrt(2x + 4) + 1 ≥ 5

Subtract 1 from both sides:
sqrt(2x + 4) ≥ 4

Now square both sides:
2x + 4 ≥ 16

Subtract 4 from both sides:
2x ≥ 12

Divide both sides by 2:
x ≥ 6

Answer 2

Simplify M^2/3 divided by M^1/5
= M^(2/3 - 1/5) = M^ (10/15 - 3/15) = M^(7/15) << answer

sqrt((2x+4)) +1 is >= 5
sqrt((2x + 4)) + 1 -1 >= 5 -1
sqrt((2x + 4)) >= 4
squaring both sides
(2x + 4) > = 16
2x + 4 - 4 >= 16 -4
2x >= 12
x >= 6 (inequality holds for all values of x greater than or equal to 6)

Answer 3

Answers and solutions without explanations, and without requiring you do do some of the work will turn your brain into mush.

a) you need to use the exponent rule that when dividing common bases you SUBTRACT the exponents. So simplify

M^(2/3 -1/5) using a LCD of 15.

b) Write sqrt(2x+4) +1 >= 5

Now isolate the sqrt on the left and everything else on the right. Square both sides to get rid of radical and then solve for x.

Answer 4

(1) M^7/15
(2) x is greater than or equal to 6

Answer 5

(M^2/3)/(M/5) = (M^2/3)(5/M) = 5M/3

Or maybe you meant

M^(2/3)/M^(1/5) = M^(2/3 - 1/5) = M^(10/15 - 3/15) = M^(7/15)


sqrt(2x + 4) + 1 >= 5

sqrt(2x + 4) >= 4

2x + 4 >= 16 {square both sides}

2x >= 12

x >= 6

Answer 6

1) M^7/15

2)x is greater than or equal to 6