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Popular >

simplify 4^{5/4}

Solution

simplify

4^{\frac{5}{4}}

Solution

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

+1

Decimal Notation

5.65685 \dots

Solution steps

4^{\frac{5}{4}}

Factor the number:

4 = 2^{2}

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

Apply exponent rule:

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

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

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

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

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

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

Apply exponent rule:

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

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

2^{2} = 4

= 4 \cdot 2^{\frac{1}{2}}

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Frequently Asked Questions (FAQ)

What is 4^{5/4} ?
The solution to 4^{5/4} is 4*2^{1/2}