Question

Simplify and also write laws which are used to simplify this (3⁻⁴× 10⁻²×81×2² ×125) ⁄ 5​

Answer 1

Answer :-

$\implies\sf \dfrac{3^{-4} \times 10^{-2} \times 81 \times 2^2 \times 125}{5}$

$\implies\sf \dfrac{3^{-4} \times (2 \times 5)^{-2} \times 3^4 \times 2^2 \times 5^3}{5}$

• $\sf (a \times b)^m = a^m \times b^m$

$\implies\sf \dfrac{3^{-4} \times 2^{-2} \times 5^{-2} \times 3^4 \times 2^2 \times 5^3}{5}$

$\implies\sf \dfrac{(3^{-4} \times 3^4) \times (2^{-2} \times 2^2) 5^{-2} \times 5^3)}{5}$

• $\sf {a^m} \times {a^n} = a^{m - n}$

$\implies\sf \dfrac{3^{-4+4} \times 2^{-2+2} \times 5^{-2+3}}{5}$

$\implies\sf \dfrac{3^0 \times 2^0 \times 5^1}{5}$

• $\sf a^0 = 1$

$\implies\sf \dfrac{1 \times 1 \times 5}{5}$

$\implies\sf \dfrac{5^1}{5^1}$

• $\sf \dfrac{a^m}{a^n} = a^{m - n}$

$\implies\sf 5^{1-1}$

$\implies\sf 5^0$

$\implies\boxed{\sf 1}$

Answer 2

✠ Yᴏᴜʀ Qᴜᴇsᴛɪᴏɴ ☟

$\\ \qquad \underline{\bf ☯ \: \: Simplify \: \rm this \: \: \tt \dfrac{ { 3 }^{ -4 } \times { 10 }^{ -2 } \times 81 \times 2 ^ { 2 } \times 125 }{ 5 }.}$

✠ Rᴇǫᴜɪʀᴇᴅ Aɴsᴡᴇʀ ☟

$\\ \\ \bigstar\: \: \underline { \boxed{ \color{purple}{ \bf \: Question \: :\to \: \tt \: \dfrac{ { 3 }^{ -4 } \times { 10 }^{ -2 } \times 81 \times 2 ^ { 2 } \times 125 }{ 5 }}}} \: \: \bigstar$

$༒ \: \: \frak{ \: \underline {Calculate \: 3 \: t o \: the \: power \: of \: -4 \: and \: get \: \dfrac{1}{81}.}}$

$: \implies \tt \: \dfrac{\dfrac{1}{81}\times 10^{-2}\times 81\times 2^{2}\times 125}{5}$

$༒ \: \: \frak{ \: \underline {Calculate \: 10 to \: the \: power \: of \: -2 \: and \: get \: \dfrac{1}{100}.}}$

$: \implies \tt \frac{\frac{1}{81}\times \left(\frac{1}{100}\right)\times 81\times 2^{2}\times 125}{5}$

$༒ \: \: \frak{ \: \underline {Multiply \: \dfrac{1}{81} \: and \: \dfrac{1}{100} \: to \: get \: \dfrac{1}{8100}.}}$

$: \implies \: \tt\frac{\frac{1}{8100}\times 81\times 2^{2}\times 125}{5}$

$༒ \: \: \frak{ \: \underline { Multiply \: \dfrac{1}{8100} \: and \: 81 \: to \: get \: \dfrac{1}{100}..}}$

$: \implies \tt \: \frac{\frac{1}{100}\times 2^{2}\times 125}{5}$

$༒ \: \: \frak{ \: \underline {Calculate \: 2 \: to \: the \: power \: of \: 2 \: and \: get \: 4.}}$

$: \implies \tt\frac{\frac{1}{100}\times 4\times 125}{5}$

$༒ \: \: \frak{ \: \underline {Multiply \: \frac{1}{100} \: a nd \: 4 \: t o \: get \: \frac{1}{25}.}}$

$: \implies \: \tt\frac{\frac{1}{25}\times 125}{5}$

$༒ \: \: \frak{ \: \underline {Multiply \: \frac{1}{25} \: and \: 125 \: to \: get \: 5.}}$

$: \implies \tt \frac{ \cancel5}{ \cancel5}$

$༒ \: \: \frak{ \: \underline {Divide \: 5 \: by \: 5 \: to \: get \: 1.}}$

$\bigstar\: \: \underline{ \boxed{ \color{purple}{}\bf Answer :\to\: 1}} \: \: \bigstar$

✬ Hope it helps u ✬