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Popular >

simplify 243^{5/2}

Solution

simplify

24 3^{\frac{5}{2}}

Solution

531441 \cdot 3^{\frac{1}{2}}

+1

Decimal Notation

920482.81322 \dots

Solution steps

24 3^{\frac{5}{2}}

Prime factorization of

243 : 3^{5}

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

Apply exponent rule:

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

3^{5} = 3^{4} \cdot 3

= (3^{4} \cdot 3)^{\frac{5}{2}}

Apply exponent rule:

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

(3^{4} \cdot 3)^{\frac{5}{2}} = (3^{4})^{\frac{5}{2}} \cdot 3^{\frac{5}{2}}

= (3^{4})^{\frac{5}{2}} \cdot 3^{\frac{5}{2}}

(3^{4})^{\frac{5}{2}} = 59049

= 59049 \cdot 3^{\frac{5}{2}}

3^{\frac{5}{2}} = 3^{2} \cdot 3^{\frac{1}{2}}

= 3^{2} \cdot 59049 \cdot 3^{\frac{1}{2}}

Factor integer

59049 = 3^{10}

= 3^{10} \cdot 3^{2} \cdot 3^{\frac{1}{2}}

Apply exponent rule:

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

3^{10} \cdot 3^{2} \cdot 3^{\frac{1}{2}} = 3^{10 + 2 + \frac{1}{2}}

= 3^{10 + 2 + \frac{1}{2}}

Add the numbers:

10 + 2 = 12

= 3^{\frac{1}{2} + 12}

Join

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

= 3^{\frac{25}{2}}

3^{\frac{25}{2}} = 3^{12 + \frac{1}{2}}

= 3^{12 + \frac{1}{2}}

Apply exponent rule:

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

= 3^{12} \cdot 3^{\frac{1}{2}}

3^{12} = 531441

= 531441 \cdot 3^{\frac{1}{2}}

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-0.8x^2+20x-62.5=0

- 0.8 x^{2} + 20 x - 62.5 = 0

Frequently Asked Questions (FAQ)

What is 243^{5/2} ?
The solution to 243^{5/2} is 531441*3^{1/2}