What is the answer to (72)/((x^{8/5))}=((x^{7/5}))/(24) ?

The answer to (72)/((x^{8/5))}=((x^{7/5}))/(24) is x=12

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(72)/((x^{8/5))}=((x^{7/5}))/(24)

\frac{72}{( x ^{\frac{8}{5}} )} = \frac{( x ^{\frac{7}{5}} )}{24}

x = 12

Solution steps

\frac{72}{( x ^{\frac{8}{5}} )} = \frac{( x ^{\frac{7}{5}} )}{24}

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

72 \cdot 24 = x^{\frac{8}{5}} x^{\frac{7}{5}}

Move

x^{\frac{8}{5}} x^{\frac{7}{5}}

to the left side

1728 - x^{\frac{8}{5}} x^{\frac{7}{5}} = 0

Factor

1728 - x^{\frac{8}{5}} x^{\frac{7}{5}} : - (x - 12) (x^{2} + 12 x + 144)

- (x - 12) (x^{2} + 12 x + 144) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 12 = 0 or x^{2} + 12 x + 144 = 0

Solve

x - 12 = 0 : x = 12

Solve

x^{2} + 12 x + 144 = 0 :

No Solution for

x \in R

x = 12

Verify Solutions:

x = 12

True

The solution is

x = 12

x^{\frac{1}{2}} - 8 x^{\frac{1}{4}} + 15 = 0

x^{2} - x = 3 - x

x + 2 x - 1 = 2

2 x^{2} - 2 6 x + 3 = 0

6 x^{2} + 7 5 x + 10 = 0

What is the answer to (72)/((x^{8/5))}=((x^{7/5}))/(24) ?
The answer to (72)/((x^{8/5))}=((x^{7/5}))/(24) is x=12
Solve for x: (72)/((x^{8/5))}=((x^{7/5}))/(24)
The solution is x=12