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Popular >

simplify 32^{5/2}

Solution

simplify

3 2^{\frac{5}{2}}

Solution

4096 \cdot 2^{\frac{1}{2}}

+1

Solution steps

3 2^{\frac{5}{2}}

Prime factorization of

32 : 2^{5}

= (2^{5})^{\frac{5}{2}}

Apply exponent rule:

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

2^{5} = 2^{4} \cdot 2

= (2^{4} \cdot 2)^{\frac{5}{2}}

Apply exponent rule:

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

(2^{4} \cdot 2)^{\frac{5}{2}} = (2^{4})^{\frac{5}{2}} \cdot 2^{\frac{5}{2}}

= (2^{4})^{\frac{5}{2}} \cdot 2^{\frac{5}{2}}

(2^{4})^{\frac{5}{2}} = 1024

= 1024 \cdot 2^{\frac{5}{2}}

2^{\frac{5}{2}} = 2^{2} \cdot 2^{\frac{1}{2}}

= 2^{2} \cdot 1024 \cdot 2^{\frac{1}{2}}

Factor integer

1024 = 2^{10}

= 2^{10} \cdot 2^{2} \cdot 2^{\frac{1}{2}}

Apply exponent rule:

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

2^{10} \cdot 2^{2} \cdot 2^{\frac{1}{2}} = 2^{10 + 2 + \frac{1}{2}}

= 2^{10 + 2 + \frac{1}{2}}

Add the numbers:

10 + 2 = 12

= 2^{\frac{1}{2} + 12}

Join

\frac{1}{2} + 12 : \frac{25}{2}

= 2^{\frac{25}{2}}

2^{\frac{25}{2}} = 2^{12 + \frac{1}{2}}

= 2^{12 + \frac{1}{2}}

Apply exponent rule:

x^{a + b} = x^{a} x^{b}

= 2^{12} \cdot 2^{\frac{1}{2}}

2^{12} = 4096

= 4096 \cdot 2^{\frac{1}{2}}

Popular Examples

factor 8v-24 factor

8 v - 24

y^{2} = 20

factor n^3+1000 factor

n^{3} + 1000

factor 4x^2-16x+7 factor

4 x^{2} - 16 x + 7

3 x - 1 = 0

Frequently Asked Questions (FAQ)

What is 32^{5/2} ?
The solution to 32^{5/2} is 4096*2^{1/2}