Darren Salas

2023-02-26

If ${(x-1)}^{\frac{2}{3}}=25$ then x equals what?

Audrina Donaldson

Beginner2023-02-27Added 6 answers

Because you must perform some challenging operations with exponents in order to isolate x, this problem might seem frightening.

But if you think about it, we can cancel out the $\frac{2}{3}$ by raising each side to $\frac{3}{2}$, because when you raise an exponent to an exponent it serves to multiply the two, and $\frac{2}{3}\cdot \frac{3}{2}=1$.

Based on this, we can raise 25 to the power of $\frac{3}{2}$, as well as $(x-1)}^{\frac{2}{3}$ in order to get the equation

$(x-1)}^{\frac{2}{3}\cdot \frac{3}{2}}={25}^{\frac{3}{2}$

$(x-1)=125$

$x=126$

But if you think about it, we can cancel out the $\frac{2}{3}$ by raising each side to $\frac{3}{2}$, because when you raise an exponent to an exponent it serves to multiply the two, and $\frac{2}{3}\cdot \frac{3}{2}=1$.

Based on this, we can raise 25 to the power of $\frac{3}{2}$, as well as $(x-1)}^{\frac{2}{3}$ in order to get the equation

$(x-1)}^{\frac{2}{3}\cdot \frac{3}{2}}={25}^{\frac{3}{2}$

$(x-1)=125$

$x=126$