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Popular >

simplify (9/2 x^{1/2})^2

Solution

simplify

(\frac{9}{2} x^{\frac{1}{2}})^{2}

Solution

\frac{81 x}{4}

Solution steps

(\frac{9}{2} x^{\frac{1}{2}})^{2}

Apply exponent rule:

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

(\frac{9}{2} x^{\frac{1}{2}})^{2} = (\frac{9}{2})^{2} (x^{\frac{1}{2}})^{2}

= (\frac{9}{2})^{2} (x^{\frac{1}{2}})^{2}

(\frac{9}{2})^{2} = \frac{81}{4}

= \frac{81}{4} (x^{\frac{1}{2}})^{2}

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

(x^{\frac{1}{2}})^{2} = x^{\frac{1}{2} \cdot 2}

= \frac{81}{4} x^{\frac{1}{2} \cdot 2}

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

= \frac{81}{4} x^{1}

Apply exponent rule:

a^{1} = a

x^{1} = x

= \frac{81}{4} x

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{81 x}{4}

Popular Examples

x^{2} - x - 12 = 0

factor 14x^3-49x^2+21x factor

14 x^{3} - 49 x^{2} + 21 x

x + 3 = 8

factor m^2-16m+64 factor

m^{2} - 16 m + 64

14 = 7 x - 7

Frequently Asked Questions (FAQ)

What is (9/2 x^{1/2})^2 ?
The solution to (9/2 x^{1/2})^2 is (81x)/4