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Popular >

simplify (27*64)^{2/3}

Solution

simplify

(27 \cdot 64)^{\frac{2}{3}}

Solution

144

Solution steps

(27 \cdot 64)^{\frac{2}{3}}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(27 \cdot 64)^{\frac{2}{3}} = 2 7^{\frac{2}{3}} \cdot 6 4^{\frac{2}{3}}

= 2 7^{\frac{2}{3}} \cdot 6 4^{\frac{2}{3}}

2 7^{\frac{2}{3}} = 9

= 9 \cdot 6 4^{\frac{2}{3}}

Factor the number:

64 = 4^{3}

= 9 (4^{3})^{\frac{2}{3}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

(4^{3})^{\frac{2}{3}} = 4^{3 \cdot \frac{2}{3}}

= 9 \cdot 4^{3 \cdot \frac{2}{3}}

3 \cdot \frac{2}{3} = 2

= 9 \cdot 4^{2}

4^{2} = 16

= 9 \cdot 16

Multiply the numbers:

9 \cdot 16 = 144

= 144

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Frequently Asked Questions (FAQ)

What is (27*64)^{2/3} ?
The solution to (27*64)^{2/3} is 144