Question

1. Express 4.5 x 10⁴ in usual form.
2. Simplify and find the reciprocal of (-2) ⁻³ x (-3)⁻³ x (4) ⁻³

Answer 1

$\large{ \pmb{ \sf{ \underline{Required \: Solution...}}}}$

We are asked to find ,

${\pmb{\sf{1) \: 4.5 \times 10^4\; in \;usual\;form.}}}$

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${{ \pmb{\sf{2)\:Simplification\:of\:(-2)^{-3}\times{(-3)}^{-3}\times{(4)}^{-3}\&\: Then\:reciprocal\:of\:answer\:the\:obtained\:}}}}$

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Accurate solution:

1) 4.5 × 10⁴

~ To solve this question we have to convert the decimal into fraction,

$\sf \implies \dfrac{45}{10} \times {10}^{4}$

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~ Now, Let's cancel 10, We get ,

$\sf \implies 45 \times {10}^{3}$

~ Let's put the value of 10³,

$\sf \implies 45 \times 1000$

~ After multiplying we get,

$\sf \implies 45000$

Henceforth, The usual form of 4.5 × 10⁴ is 45000.

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2) 2. Simplify and find the reciprocal of (-2)⁻³ × (-3)⁻³ × (4)⁻³

Explanation:

~ To solve this question we have to simplify (-2)⁻³ × (-3)⁻³ × (4)⁻³ first, Let's make the powers positive,

${\sf{\Rightarrow { - 2}^{ - 3} = {\dfrac{ - 1}{2}}^{3} }}$

${\sf{\Rightarrow { - 3}^{ - 3} = {\dfrac{ - 1}{3}}^{3} }}$

${\sf{\Rightarrow { 4}^{ - 3} = {\dfrac{ 1}{4}}^{3} }}$

~ Here, Powers are same. Thus, We can take it as common,

${\sf{{\Rightarrow \left (\dfrac{ - 1}{2} \times \dfrac{ - 1}{3} \times \dfrac{ 1}{4}\right)}^{3} }}$

~ Multiplying the fractions,

${\sf{{\Rightarrow {\dfrac{1}{24} }^{3} }}}$

~ Now let's reciprocal this,

${\sf{{\Rightarrow {24}^{3} }}}$

${\sf{{\Rightarrow 13824 }}}$

Henceforth, The required answer is 13824.

$\large{ \pmb{ \sf{ \underline{Additional \: information...}}}}$

• Reciprocal - The reciprocal of the number is the multiplicative inverse of it.

Example - Reciprocal of $\sf \frac{3}{5}$ is $\sf \frac{5}{3}$

• Usual form - The exponential form/fractional form expressed in numerical form is called usual form.