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Popular >

simplify 64^{3/4}

Solution

simplify

6 4^{\frac{3}{4}}

Solution

16 \cdot 2^{\frac{1}{2}}

+1

Decimal Notation

22.62741 \dots

Solution steps

6 4^{\frac{3}{4}}

Prime factorization of

64 : 2^{6}

= (2^{6})^{\frac{3}{4}}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

2^{6} = 2^{4} \cdot 2^{2}

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

Apply exponent rule:

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

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

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

(2^{4})^{\frac{3}{4}} = 8

= 8 (2^{2})^{\frac{3}{4}}

Apply exponent rule:

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

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

= 8 \cdot 2^{2 \cdot \frac{3}{4}}

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

= 8 \cdot 2^{\frac{3}{2}}

2^{\frac{3}{2}} = 2 \cdot 2^{\frac{1}{2}}

= 8 \cdot 2 \cdot 2^{\frac{1}{2}}

Multiply the numbers:

8 \cdot 2 = 16

= 16 \cdot 2^{\frac{1}{2}}

Popular Examples

factor x^4+11x^2+24 factor

x^{4} + 11 x^{2} + 24

4 x^{2} + 7 x - 2 = 0

factor 12x^2+17x+6 factor

12 x^{2} + 17 x + 6

2 (12 - 8 x) = x - 11 x

simplify-i^2 simplify

- i^{2}

Frequently Asked Questions (FAQ)

What is 64^{3/4} ?
The solution to 64^{3/4} is 16*2^{1/2}