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Popular >

simplify 256^{4/3}

Solution

simplify

25 6^{\frac{4}{3}}

Solution

1024 \cdot 2^{\frac{2}{3}}

+1

Decimal Notation

1625.49867 \dots

Solution steps

25 6^{\frac{4}{3}}

Prime factorization of

256 : 2^{8}

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

Apply exponent rule:

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

2^{8} = 2^{6} \cdot 2^{2}

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

Apply exponent rule:

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

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

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

(2^{6})^{\frac{4}{3}} = 256

= 256 (2^{2})^{\frac{4}{3}}

Apply exponent rule:

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

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

= 256 \cdot 2^{2 \cdot \frac{4}{3}}

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

= 256 \cdot 2^{\frac{8}{3}}

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

= 256 \cdot 4 \cdot 2^{\frac{2}{3}}

Multiply the numbers:

256 \cdot 4 = 1024

= 1024 \cdot 2^{\frac{2}{3}}

Popular Examples

- x^{2} + x + 8 = 3

2 - 2 x^{2} = - 8

simplify 2/5+2/8 simplify

\frac{2}{5} + \frac{2}{8}

3(4x+3)=2x-5(3-x)+2

3 (4 x + 3) = 2 x - 5 (3 - x) + 2

factor 4a^2-ac factor

4 a^{2} - a c

Frequently Asked Questions (FAQ)

What is 256^{4/3} ?
The solution to 256^{4/3} is 1024*2^{2/3}