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Popular >

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

Solution

simplify

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

Solution

\frac{9 t}{4}

Solution steps

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

Apply exponent rule:

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

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

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

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

= \frac{9}{4} (t^{\frac{1}{2}})^{2}

Apply exponent rule:

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

assuming

a \geq 0

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

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

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

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

Apply exponent rule:

a^{1} = a

t^{1} = t

= \frac{9}{4} t

Multiply fractions:

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

= \frac{9 t}{4}

Popular Examples

\frac{7 x - 5}{9} = - 6

3 x - 3 = x + 5

3 x - 4 > 11

17 \leq 5 x - 3 \leq 22

2 x - 3 = 4 x + 9

Frequently Asked Questions (FAQ)

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