What is (1 9/16)^{3/2} ?

The solution to (1 9/16)^{3/2} is 1 61/64

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simplify (1 9/16)^{3/2}

simplify

(1 \frac{9}{16})^{\frac{3}{2}}

1 \frac{61}{64}

Decimal

1.953125

Solution steps

(1 \frac{9}{16})^{\frac{3}{2}}

Convert mixed numbers to improper fractions:

1 \frac{9}{16} = \frac{25}{16}

= (\frac{25}{16})^{\frac{3}{2}}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{2 5 ^{\frac{3}{2}}}{1 6 ^{\frac{3}{2}}}

2 5^{\frac{3}{2}} = 125

= \frac{125}{1 6 ^{\frac{3}{2}}}

1 6^{\frac{3}{2}} = 64

= \frac{125}{64}

Convert improper fractions to mixed numbers:

\frac{125}{64} = 1 \frac{61}{64}

= 1 \frac{61}{64}

c x^{2} + c y^{2} - w x^{2} - w y^{2} + w - c

15 x^{2} - 8 x - 12

\frac{2}{x - 1} \geq - 1

\frac{5 ( x - 4 )}{2} \geq \frac{2 x}{3} - 15

- \frac{2}{3} < r - \frac{2}{3}