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Popular >

simplify 8^{5/2}

Solution

simplify

8^{\frac{5}{2}}

Solution

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

+1

Solution steps

8^{\frac{5}{2}}

Prime factorization of

8 : 2^{3}

= (2^{3})^{\frac{5}{2}}

Apply exponent rule:

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

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

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

Apply exponent rule:

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

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

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

(2^{2})^{\frac{5}{2}} = 32

= 32 \cdot 2^{\frac{5}{2}}

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

= 2^{2} \cdot 32 \cdot 2^{\frac{1}{2}}

Factor integer

32 = 2^{5}

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

Apply exponent rule:

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

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

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

Add the numbers:

5 + 2 = 7

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

Join

\frac{1}{2} + 7 : \frac{15}{2}

= 2^{\frac{15}{2}}

2^{\frac{15}{2}} = 2^{7 + \frac{1}{2}}

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

Apply exponent rule:

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

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

2^{7} = 128

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

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Frequently Asked Questions (FAQ)

What is 8^{5/2} ?
The solution to 8^{5/2} is 128*2^{1/2}