en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 8^{7/2}

Solution

simplify

8^{\frac{7}{2}}

Solution

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

+1

Decimal Notation

1448.15468 \dots

Solution steps

8^{\frac{7}{2}}

Prime factorization of

8 : 2^{3}

= (2^{3})^{\frac{7}{2}}

Apply exponent rule:

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

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

= (2^{2} \cdot 2)^{\frac{7}{2}}

Apply exponent rule:

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

(2^{2} \cdot 2)^{\frac{7}{2}} = (2^{2})^{\frac{7}{2}} \cdot 2^{\frac{7}{2}}

= (2^{2})^{\frac{7}{2}} \cdot 2^{\frac{7}{2}}

(2^{2})^{\frac{7}{2}} = 128

= 128 \cdot 2^{\frac{7}{2}}

2^{\frac{7}{2}} = 2^{3} \cdot 2^{\frac{1}{2}}

= 2^{3} \cdot 128 \cdot 2^{\frac{1}{2}}

Factor integer

128 = 2^{7}

= 2^{7} \cdot 2^{3} \cdot 2^{\frac{1}{2}}

Apply exponent rule:

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

2^{7} \cdot 2^{3} \cdot 2^{\frac{1}{2}} = 2^{7 + 3 + \frac{1}{2}}

= 2^{7 + 3 + \frac{1}{2}}

Add the numbers:

7 + 3 = 10

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

Join

\frac{1}{2} + 10 : \frac{21}{2}

= 2^{\frac{21}{2}}

2^{\frac{21}{2}} = 2^{10 + \frac{1}{2}}

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

Apply exponent rule:

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

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

2^{10} = 1024

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

Popular Examples

factor (a+b)^2-m^2 factor

(a + b)^{2} - m^{2}

4 x^{2} + 7 x - 9 = 0

\frac{3}{4} = m + \frac{1}{4}

factor n^2+n-2 factor

n^{2} + n - 2

simplify (-9)^{-2}simplify

(- 9)^{- 2}

Frequently Asked Questions (FAQ)

What is 8^{7/2} ?
The solution to 8^{7/2} is 1024*2^{1/2}