How do you simplify $64^{\frac{3}{4}} \times 81^{\frac{2}{3}}$ $64^(3/4)times81^(2/3)$ ?

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Answer 1 · 2017-05-23T19:49:30

$144 \cdot 2^{\frac{1}{2}} \cdot 3^{\frac{2}{3}}$ $144*2^(1/2)*3^(2/3)$

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

$64^{\frac{3}{4}} \times 81^{\frac{2}{3}} = {(2^{6})}^{\frac{3}{4}} \times {(3^{4})}^{\frac{2}{3}}$ $64^(3/4)xx81^(2/3)=(2^6)^(3/4)xx(3^4)^(2/3)$

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

${(2^{2} \cdot 2^{4})}^{\frac{3}{4}} \times {(3^{1} \cdot 3^{3})}^{\frac{2}{3}}$ $(2^2*2^4)^(3/4)xx(3^1*3^3)^(2/3)$

Step 3. Multiply the fractional powers through

$(2^{\frac{3}{2}} \cdot 2^{3}) \times (3^{\frac{2}{3}} \cdot 3^{2})$ $(2^(3/2)*2^3)xx(3^(2/3)*3^2)$

$({(2 \cdot 2^{2})}^{\frac{1}{2}} \cdot 2^{3}) \times (3^{\frac{2}{3}} \cdot 3^{2})$ $((2*2^2)^(1/2)*2^3)xx(3^(2/3)*3^2)$

$(2^{\frac{1}{2}} \cdot 2 \cdot 2^{3}) \times (3^{\frac{2}{3}} \cdot 3^{2})$ $(2^(1/2)*2*2^3)xx(3^(2/3)*3^2)$

$144 \cdot 2^{\frac{1}{2}} \cdot 3^{\frac{2}{3}}$ $144*2^(1/2)*3^(2/3)$

How do you simplify 6434×812364^(3/4)times81^(2/3)?