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Popular >

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

Solution

simplify

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

Solution

\frac{9 x}{4}

Solution steps

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

Apply exponent rule:

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

(\frac{3}{2} x^{\frac{1}{2}})^{2} = (\frac{3}{2})^{2} (x^{\frac{1}{2}})^{2}

= (\frac{3}{2})^{2} (x^{\frac{1}{2}})^{2}

(\frac{3}{2})^{2} = \frac{9}{4}

= \frac{9}{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{9}{4} x^{\frac{1}{2} \cdot 2}

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

= \frac{9}{4} x^{1}

Apply exponent rule:

a^{1} = a

x^{1} = x

= \frac{9}{4} x

Multiply fractions:

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

= \frac{9 x}{4}

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\frac{3}{4} \cdot \frac{1}{4}

2 x - 15 \leq 5

Frequently Asked Questions (FAQ)

What is (3/2 x^{1/2})^2 ?
The solution to (3/2 x^{1/2})^2 is (9x)/4