Please disable adblock in order to continue browsing our website.

Unfortunately, in the last year, adblock has now begun disabling almost all images from loading on our site, which has lead to mathwarehouse becoming unusable for adlbock users.

How to solve Fraction Exponents

Exponential Equations with a radical in the exponent

Before attemptng to solve rational exponential equations like $$x ^{\frac{2}{3}} + 1 = 65$$, you should be comfortable

Steps

• Isolate the expression with the fractional exponent
• Raise both sides to multiplicative inverse of the exponent
• simplify
Example 1

Solve $$x ^{\frac{2}{3}} +1 = 65$$

Step 1

Isolate fraction exponent

Step 2

Raise both sides to multiplicative inverse of the exponent

$$\left( x ^{\frac 2 3} \right)^{\red{\frac 3 2}} = 64^{\red{\frac 3 2}}$$
Step 2
$$x = 64^{\red{\frac 3 2}} \\ x = 512$$