Question

Simplify and express each of the following in exponential form:

(1). 2³× 3⁴×4/3×32
(2). {(5²)³×5⁴}÷5⁷
(3). 25⁴×5³
(4). 3×7²×11⁸/21×11³
(5). 3⁷/3⁴×3³
(6). 2⁰+3⁰+4⁰
(7). 2⁰×3⁰×4⁰
(8). (3⁰+2⁹)×5⁰
(9). 2⁸×a⁵/4³×a³
(10). (a⁵/a³)×a⁸
(11). 4⁵×a⁸b³/4⁵×a⁵b²
(12). (2³×2)²
Thankyou!​

Answer 1

Explanation:

`\bf \underline{➤ Answer\: (1)-} \\`

`{\tt \longrightarrow \frac{{2}^(3) * {3}^(4) * 4}{3 * 32}}`

Convert all of them into exponents and powers form.

`{\tt \longrightarrow \frac{{2}^(3) * {3}^(4) * {2}^(2)}{{3}^(1) * {2}^(5)}}`

Simplify each of them...

`{\tt \longrightarrow \frac{{2}^(3 + 2) * {3}^(4)}{{3}^(1) * {2}^(5)} = \frac{{2}^(5) * {3}^(4)}{{3}^(1) * {2}^(5)}}`

`{\tt \longrightarrow {2}^(5 - 5) * {3}^(4 - 1) = {2}^(0) * {3}^(3)}`

`{\tt \longrightarrow {3}^(3)}`

`\bf \underline{➤ Answer\: (2)-} \\`

`{\tt \longrightarrow \bigg(( {5}^(2) {)}^(3) * {5}^(4) \bigg) / {5}^(7)}`

`{\tt \longrightarrow \bigg({5}^(2 * 3)* {5}^(4) \bigg) / {5}^(7)}`

`{\tt \longrightarrow {5}^(6 + 4) / {5}^(7) = {5}^(10) / {5}^(7)}`

`{\tt \longrightarrow {5}^(10 - 7)}`

`{\tt \longrightarrow {5}^(3)}`

`\bf \underline{➤ Answer\: (3)-} \\`

`{\tt \longrightarrow {25}^(4) * {5}^(3)}`

`{\tt \longrightarrow ( {5}^(2))^(4) * {5}^(3) = {5}^(2 * 4) * {5}^(3)}`

`{\tt \longrightarrow {5}^(8) * {5}^(3) = {5}^(8 + 3)}`

`{\tt \longrightarrow {5}^(11)}`

`\bf \underline{➤ Answer\: (4)-} \\`

`\tt \longrightarrow \frac{3 * {7}^(2) * {11}^(8)}{21 * {11}^(3)}`

`\tt \longrightarrow \frac{{3}^(1) * {7}^(2) * {11}^(8)}{ {7}^(1) * {3}^(1) * {11}^(3)}`

`{\tt \longrightarrow {3}^(1 - 1) * {7}^(2 - 1) * {11}^(8 - 3)}`

`{\tt \longrightarrow {3}^(0) * {7}^(1) * {11}^(5)}`

`{\tt \longrightarrow {7}^(1) * {11}^(5)}`

`\bf \underline{➤ Answer\: (5)-} \\`

`\tt \longrightarrow \frac{{3}^(7)}{ {3}^(4) * {3}^(3)}`

`\tt \longrightarrow \frac{{3}^(7)}{ {3}^(4 + 3)} = \frac{{3}^(7)}{{3}^(7)}`

`\tt \longrightarrow {3}^(7 - 7)`

`\tt \longrightarrow {3}^(0)`

`\bf \underline{➤ Answer\: (6)-} \\`

`{\tt \longrightarrow {2}^(0) + {3}^(0) + {4}^(0)}`

`{\tt \longrightarrow 1 + 1 + 1 = 3}`

`{\tt \longrightarrow {3}^(1)}`

`\bf \underline{➤ Answer\: (7)-} \\`

`{\tt \longrightarrow {2}^(0) * {3}^(0) * {4}^(0)}`

`{\tt \longrightarrow 1 * 1 * 1 = 1}`

`{\tt \longrightarrow {1}^(1)}`

`\bf \underline{➤ Answer\: (8)-} \\`

`{\tt \longrightarrow ({3}^(0) + {2}^(0)) * {5}^(0)}`

`{\tt \longrightarrow (1 + 1) * 1 = 2 * 1}`

`{\tt \longrightarrow {2}^(1)}`

`\bf \underline{➤ Answer\: (9)-} \\`

`\tt \longrightarrow \frac{{2}^(8) * {a}^(5)}{{4}^(3) * {a}^(3)}`

`\tt \longrightarrow \frac{{2}^(8) * {a}^(5)}{( {2}^(2){)}^(3) * {a}^(3)}`

`\tt \longrightarrow \frac{{2}^(8) * {a}^(5)}{{2}^(2 * 3) * {a}^(3)} = \frac{{2}^(8) * {a}^(5)}{{2}^(6) * {a}^(3)}`

`\tt \longrightarrow {2}^(8 - 6) * {a}^(5 - 3)`

`\tt \longrightarrow {2}^(2) * {a}^(2)`

`\bf \underline{➤ Answer\: (10)-} \\`

`{\tt \longrightarrow \bigg(\frac{{a}^(5)}{{a}^(3)} \bigg) * {a}^(8)}`

`{\tt \longrightarrow {a}^(5 - 3) * {a}^(8)}`

`{\tt \longrightarrow {a}^(2) * {a}^(8) = {a}^(2 + 8)}`

`{\tt \longrightarrow {a}^(10)}`

`\bf \underline{➤ Answer\: (11)-} \\`

`{\tt \longrightarrow \frac{{4}^(5) * {a}^(8) \: {b}^(3)}{{4}^(5) * {a}^(5) \: {b}^(2)}}`

`{\tt \longrightarrow {4}^(5 - 5) * {a}^(8 - 5) * {b}^(3 - 2)}`

`{\tt \longrightarrow {4}^(0) * {a}^(3) * {b}^(1)}`

`{\tt \longrightarrow {a}^(3) * {b}^(1)}`

`\bf \underline{➤ Answer\: (12)-} \\`

`{\tt \longrightarrow \bigg( {2}^(3) * 2 \bigg)^(2)}`

`{\tt \longrightarrow \bigg( {2}^(3 + 1)\bigg)^(2) = {2}^(4 * 2)}`

`{\tt \longrightarrow {2}^(8)}`

━━━━━━━━━━━━━━━━━━━━━

`\bf \underline{Used \:Laws\: of \:Intergal\:Exponents-} \\`

`{\to \sf {a}^(m) * {a}^(n) = {a}^(m + n)}`

`{\to \sf {a}^(m) / {a}^(n) = {a}^(m - n)}`

`{\to \sf \bigg( {a}^(m) \bigg)^(n) = {a}^(m * n)}`

`{\to \sf \frac{ {a}^(m)}{ {b}^(m)} = \bigg( {(a)/(b)}\bigg)^(m)}`

`{\to \sf {a}^(0) = 1}`
`{\to \sf {a}^( - 1) = (1)/(a)}`

`\textsf{Hope this helps!!}\\`