Rational Exponents

Rational Exponents

Fractional Exponents. A rational exponent represents both an integer exponent and an nth root. 

Desmos scientific calculator

•  $a^b\$  is the exponent key

•  $\frac{a}{b}$  fractional exponent

Simplify

•  $16^{\frac{1}{2}}\ =\sqrt{16}\ =\ 4$  

•  $81^{\frac{1}{2}}\ =\ \sqrt{81}\ =\ 9$  

•  $8^{\frac{1}{3}}\ =\ 2$  

•  $27^{\frac{1}{3}}\ =\ 3$  

•  $81^{\frac{1}{4}}\ =\ 3$  

Simplify

•  $16^{\frac{3}{2}}\ =\ 64$  

•  $81^{\frac{3}{2}}\ =\ 729$  

•  $8^{\frac{5}{3}}\ =\ 32$  

•  $27^{\frac{4}{3}}\ =\ 81$  

•  $81^{\frac{3}{4}}\ =\ 27$  

Fill in the Blanks

 $36^{\frac{1}{2}}\ =$  

Fill in the Blanks

 $36^{\frac{3}{2}}\ =$  

Fill in the Blanks

 $25^{\frac{5}{2}}\ =$  

Fill in the Blanks

 $27^{\frac{5}{3}}\ =$  

Fill in the Blanks

 $8^{\frac{7}{3}}\ =$  

 $\sqrt{2x-3}=9$  

•  $\left(2x-3\right)^{\frac{1}{2}}=9$  

•  $\left(\left(2x-3\right)^{\frac{1}{2}}\right)^{\frac{2}{1}}=\left(9\right)^{\frac{2}{1}}$  

•  $2x-3\ =\ 81$  

• 2x = 84

• x = 42

 $-646=-3\left(65-n\right)^{\frac{3}{2}}+2$  

•  $-648=-3\left(65-n\right)^{\frac{3}{2}}$  

•  $216=\left(65-n\right)^{\frac{3}{2}}$  

•  $\left(216\right)^{\frac{2}{3}}=\left(\left(65-n\right)^{\frac{3}{2}}\right)^{\frac{2}{3}}$  

•  $36=65-n$  

• -29 = -n

• 29 = n

Fill in the Blanks

 $27=x^{\frac{3}{2}}$  

Fill in the Blanks

 $7=x^{\frac{1}{2}}$  

Fill in the Blanks

 $6=\left(x-2\right)^{\frac{1}{2}}-3$  

Fill in the Blanks

 $3646=1+5\left(4x+17\right)^{\frac{3}{2}}$  

Poll

So, how about those Rational Exponents?

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