Question

if x=(3/2)²×(2/3)-⁴,find the value of x
​

Answer 1

Answer:

x=2

Step-by-step explanation:

x=9/4*16/81

x=2

hope it helps ☺️☺️

Answer 2

$\Large{\bold{\blue{\underline{\red{A}\pink{ns}\green{we}\purple{r:-}}}}}$

$\rm{\mapsto The \: value \: x \: is \: 11.39.}$

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$\Large{\bold{\pink{\underline{\green{G}\purple{iv}\orange{en}\red{:-}}}}}$

$\displaystyle{\rm{\leadsto x = {\bigg(\frac{3}{2} \bigg)}^{2} \times }{\bigg(\frac{2}{3} \bigg)}^{ - 4}}$

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$\Large{\bold{\blue{\underline{\red{To}\:\pink{Fin}\green{d}\purple{:-}}}}}$

$\rm{\leadsto The \: value \: x = \: ?}$

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$\Large{\bold{\pink{\underline{\red{So}\purple{lut}\green{ion}\orange{:-}}}}}$

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$\displaystyle{\tt{:\implies x = {\bigg(\frac{3}{2} \bigg)}^{2} \times }{\bigg(\frac{2}{3} \bigg)}^{ - 4}}$

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When raising a fraction to the power, raise the numerator and denominator each to the power,

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$\displaystyle{\tt{:\implies x = \frac{ {3}^{2} }{ {2}^{2} } \times }{\bigg(\frac{2}{3} \bigg)}^{ - 4}}$

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Calculate the power,

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$\displaystyle{\tt{:\implies x= \frac{9}{4} \times }{\bigg(\frac{2}{3} \bigg)}^{ - 4}}$

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When raising a fraction to the power, raise the numerator and denominator each to the power,

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$\displaystyle{\tt{:\implies x =\frac{9}{4} \times }\frac{ {2}^{ - 4} }{ {3}^{ - 4} }}$

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If the exponent is negative, change it to fraction,

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$\displaystyle{\tt{:\implies x = \frac{9}{4} \times } \frac{ \frac{1}{ {2}^{ 4} } }{ {3}^{ - 4} } }$

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Arrange the expression of the complex fraction,

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$\displaystyle{\tt{:\implies x = \frac{9}{4} \times \frac{1}{ {2}^{4} \times {3}^{ - 4} } }}$

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Calculate the power,

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$\displaystyle{\tt{:\implies x= \frac{9}{4} \times \frac{1}{ 16\times {3}^{ - 4} } }}$

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If the exponent is negative, change it to fraction,

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$\displaystyle{\tt{:\implies x = \frac{9}{4} \times \frac{1}{ 16\times \frac{1}{ {3}^{4} } } }}$

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Calculate the power,

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$\displaystyle{\tt{:\implies x = \frac{9}{4} \times \frac{1}{ 16\times \frac{1}{81} } }}$

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Natural number can be expressed as a fraction with a denominator 1,

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$\displaystyle{\tt{:\implies x = \frac{9}{4} \times \frac{1}{ \frac{16}{1} \times \frac{1}{81} } }}$

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Numerator multiply between numerator, and denominator multiply between denominators,

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$\displaystyle{\tt{:\implies x = \frac{9}{4} \times \frac{1}{ \frac{16 \times 1}{1 \times 81}} }}$

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Multiply any number by 1 does not change the value,

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$\displaystyle{\tt{:\implies x = \frac{9}{4} \times \frac{1}{ \frac{16}{1 \times 81}} }}$

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Multiply any number by 1 does not change the value,

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$\displaystyle{\tt{:\implies x = \frac{9}{4} \times \frac{1}{ \frac{16}{81}} }}$

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Calculate the complex fraction,

$\displaystyle{\tt{:\implies x = \frac{9}{4} \times \frac{81}{16} }}$

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Numerator multiply between numerator, and denominator multiply between denominators,

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$\displaystyle{\tt{:\implies x = \frac{9 \times 81}{4 \times 16} }}$

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Multiply 9 and 81,

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$\displaystyle{\tt{:\implies x = \frac{729}{4 \times 16} }}$

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Multiply 4 and 16,

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$\displaystyle{\tt{:\implies x = \frac{729}{64} }}$

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Divide the expression,

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$\displaystyle{\bf{:\implies \red{\boxed{\blue{\bf{x = 11.39}}}}}}$

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$\textsf{\textbf{\underline{Hence, the value of x is 11.39.}}}$