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Popular >

simplify (4^{1/2})(2^{3/2})

Solution

simplify

(4^{\frac{1}{2}}) (2^{\frac{3}{2}})

Solution

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

+1

Decimal Notation

5.65685 \dots

Solution steps

(4^{\frac{1}{2}}) (2^{\frac{3}{2}})

(4^{\frac{1}{2}}) (2^{\frac{3}{2}}) = 4^{\frac{1}{2}} \cdot 2^{\frac{3}{2}}

= 4^{\frac{1}{2}} \cdot 2^{\frac{3}{2}}

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

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

Apply exponent rule:

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

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

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

1 + \frac{3}{2} = \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^{1/2})(2^{3/2}) ?
The solution to (4^{1/2})(2^{3/2}) is 4*2^{1/2}