Math, asked by adaditya2007, 10 months ago

The expreesion for 4^-3 as a power with the base 2 is

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Answered by riddhimasinghal27

Answer:

Answer is 2^-6

Step-by-step explanation:

(4)^-3

(2^2)^-3

(2)^2*-3

(2)^-6

Answered by Mihir1001

$\huge{\underline{\mathfrak{\textcolor{blue}{Answer :}}}}$

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$\LARGE{\underline{\mathrm{\textcolor{red}{Step-by-step \: \: explanation :}}}}$

$\LARGE{\underline{\mathtt{\textcolor{violet}{Given :-}}}}$

$\LARGE{ {(4)}^{ - \frac{3}{2}}}$

$\LARGE{\underline{\mathtt{\textcolor{green}{To \: \: find :-}}}}$

Simplification

$\LARGE{\underline{\mathtt{\textcolor{teal}{Concept \: \: used :-}}}}$

Exponentiation

$\LARGE{\underline{\mathtt{\textcolor{blue}{Solution :-}}}}$

We have,

$\Large{ \implies {4}^{ - \frac{3}{2} } }$

$\Large{ = {( \frac{1}{4} )}^{ \frac{3}{2} } }$

$\Large{ = {( \frac{1}{4} )}^{( \frac{1}{2} \times 3)} }$

$\Large{ = {( \sqrt{ \frac{1}{4} } )}^{3} }$

$\Large{ = {( \frac{ \sqrt{1} }{ \sqrt{4} } )}^{3} }$

$\Large{ = {( \frac{1}{2} )}^{3} }$

$\Large{ = \frac{ {1}^{3} }{ {2}^{3} } }$

$\Large{ = \frac{1 \times 1 \times 1}{2 \times 2 \times 2} }$

$\Large{ = \frac{1}{8} }$

$\LARGE{\underline{\mathtt{\textcolor{magenta}{Conclusion :-}}}}$

$\LARGE{ {(4)}^{ - \frac{3}{2}} = \frac{1}{8} }$

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