How do you simplify #64^(3/4)times81^(2/3)#?

Question

Isaiah Anthony · Accepted Answer

#144*2^(1/2)*3^(2/3)#

Step 1. Find the factors of 64 and 81 #64=2^6# #81=3^4#

#64^(3/4)xx81^(2/3)=(2^6)^(3/4)xx(3^4)^(2/3)#

Step 2. Rewrite the base numbers with powers that will reduce with the fractional exponents

#(2^2*2^4)^(3/4)xx(3^1*3^3)^(2/3)#

Step 3. Multiply the fractional powers through

#(2^(3/2)*2^3)xx(3^(2/3)*3^2)#

#((2*2^2)^(1/2)*2^3)xx(3^(2/3)*3^2)#

#(2^(1/2)*2*2^3)xx(3^(2/3)*3^2)#

#144*2^(1/2)*3^(2/3)#

Abigail Allen · Answer

undefined To simplify $ 64^{\frac{3}{4}} \times 81^{\frac{2}{3}} $, first rewrite the numbers as powers of their prime factors: $ 64 = 2^6 $ and $ 81 = 3^4 $. Then apply the laws of exponents to simplify each term individually. $ 64^{\frac{3}{4}} = (2^6)^{\frac{3}{4}} = 2^{6 \times \frac{3}{4}} = 2^{\frac{18}{4}} = 2^{\frac{9}{2}} $. Similarly, $ 81^{\frac{2}{3}} = (3^4)^{\frac{2}{3}} = 3^{4 \times \frac{2}{3}} = 3^{\frac{8}{3}} $. Then multiply the simplified terms together: $ 2^{\frac{9}{2}} \times 3^{\frac{8}{3}} $.