Exponents and powers solve for x

Question

Can you help solve for x? 

A) -5+3x^7/4=379

 

B) (x^-4/5)/(5)=125

Answer 1

A)

 

-5 + 3x^(7/4) = 379

 

 

Add 5 on both sides of the equation.

 

3x^(7/4) = 384

 

 

Divide both sides of the equation by 3.

 

x^(7/4) = 128

 

 

Raise both sides of the equation to the power of 4/7.

 

x = 128^(4/7)

 

 

Rewrite 128 so that it has factors of common base.

 

x = (16 * 8)^(4/7)

 

x = (2⁴ * 2³)^(4/7)

 

x = (2⁷)^(4/7)

 

 

Applying the rules of exponents,

 

x = 2⁴

 

x = 16

 

 

 

B)

 

(x^-4/5) / 5 = 125

 

 

Rewrite 125 using the base of 5.

 

(x^-4/5) / 5 = 5³

 

 

Multiply both sides of the equation by 5.

 

x^-4/5 = 5⁴

 

 

Raise both sides of the equation to the power of -5/4.

 

x = (5⁴)^-5/4

 

x = 5^-5

 

x = 1 / 5⁵

 

x = 1 / 3125