Question

Do question no 46
Explain also​

Answer 1

Answer:

x^3

Step-by-step explanation:

{(x^a)^b}^(1/ab) {(x^b)^c}^(1/bc) {(x^c)^a}^(1/ca)

x^1 x^1 x^1

x^(1+1+1)

x^3

Answer 2

$\texttt{\textsf{\large{\underline{Solution}:}}}$

We have to simplify the expression.

Given:

$\sf = \bigg\{ \big( {x}^{a} \big)^{b} \bigg\}^{ \dfrac{1}{ab} } \cdot\bigg\{ \big( {x}^{b} \big)^{c} \bigg\}^{ \dfrac{1}{bc} } \cdot\bigg\{ \big( {x}^{c} \big)^{a} \bigg\}^{ \dfrac{1}{ca} }$

As we know that:

$\sf \implies {( {x}^{a} )}^{b} = {x}^{ab}$

We get:

$\sf = \bigg\{ {x}^{ab} \bigg\}^{ \dfrac{1}{ab} } \cdot\bigg\{ {x}^{bc}\bigg\}^{ \dfrac{1}{bc} } \cdot\bigg\{{x}^{ac}\bigg\}^{ \dfrac{1}{ca} }$

Again, using same formula, we get,

$\sf = {x}^{1} \cdot {x}^{1} \cdot {x}^{1}$

As we know that:

$\sf \implies {x}^{a} \times {x}^{b} = {x}^{a + b}$

We get:

$\sf = {x}^{1 + 1 + 1}$

$\sf = {x}^{3}$

Which is our required answer.

$\texttt{\textsf{\large{\underline{Answer}:}}}$

• Result = x³.

$\texttt{\textsf{\large{\underline{More To Know}:}}}$

If a, b are positive real numbers and m, n are rational numbers, then the following results hold -

$\sf 1. \: \: {a}^{m} \times {a}^{n} = {a}^{m + n}$

$\sf 2. \: \: ({a}^{m})^{n} = {a}^{mn}$

$\sf 3. \: \: \dfrac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n}$

$\sf4. \: \: {a}^{m} \times {b}^{m} = {(ab)}^{m}$

$\sf5. \: \: \bigg(\dfrac{a}{b} \bigg)^{m} = \dfrac{ {a}^{m} }{ {b}^{m} }$

$\sf6. \: \: {a}^{ - n} = \dfrac{1}{ {a}^{n} }$

$\sf7. \: \: {a}^{n} = {b}^{n} \rightarrow a = b, n \neq0$

$\sf8. \: \: {a}^{m} = {a}^{n} \rightarrow m = n, a \neq 1$