Which expressions are equivalent to 2 to the power of 5 / 6 to the power of 5
1. 1/3
2. 3 to the power of -5
3. (-4) to the power of -5
4. 2 to the 5th power times 6 to the -5 power

2. 3 to the power of -5

4. 2 to the 5th power times 6 to the -5 power

Step-by-step explanation:

(2⁵)/(6⁵)

(2/6)⁵

(1/3)⁵

(3^-1)⁵

3^(-5)

(2/6)⁵

2⁵ × (6^-1)⁵

2⁵ × (6^-5)

Steps to solve:

2^5/6^5

~Apply exponent rules

(1/3)^5

1^5/3^5

~Simplify

1/243

Now, we can solve for each option.

Option 1:

1/3 ≠ 1/243

This is incorrect.

Option 2:

3^-5 = 1/243

This is correct.

Option 3:

-4^-5

-1/4^5

-1/1024 ≠ 1/243

This is incorrect.

Option 4:

2^5 * 6^-5

2^5 * 1/6^5

2^5/6^5

1^5/3^5

1/243 = 1/243

This is correct.

Therefore, the correct answers are options 2 and 4.

Best of Luck!

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form