For any positive real number x- find the value ofx a x b a-b - x b x c b-cx x c x a c-a

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Standard XII

Mathematics

Scalar Matrix

For any posit...

Question

For any positive real number x, find the value of

${(\frac{x^{a}}{x^{b}})}^{a + b} \times {(\frac{x^{b}}{x^{c}})}^{b + c} \times {(\frac{x^{c}}{x^{a}})}^{c + a}$

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Solution

We have to find the value of L =

By using rational exponents, we get

By using rational exponents we get

By definition we can write as 1

Hence the value of expression is .

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For any positive real number x, find the value of ${(\frac{x^{a}}{x^{b}})}^{a + b} \times {(\frac{x^{b}}{x^{c}})}^{b + c} \times {(\frac{x^{c}}{x^{a}})}^{c + a}$

Q. For any positive real number x, write the value of

{\{{(x^{a})}^{b}\}}^{\frac{1}{a b}} {\{{(x^{b})}^{c}\}}^{\frac{1}{b c}} {\{{(x^{c})}^{a}\}}^{\frac{1}{c a}}

For any positive real number x, write the value of

${(x^{a})^{b}}^{\frac{1}{a b}} {(x^{b})^{c}}^{\frac{1}{b c}} {(x^{c})^{a}}^{\frac{1}{c a}}$

Q. For

y = l o g_{a} x

to be defined 'a' must be

Q. For

y = l o g_{a} x

to be defined 'a' must be

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For any positive real number x, find the value of xaxba+b×xbxcb+c×xcxac+a

We have to find the value of L = By using rational exponents, we get By using rational exponents we get By definition we can write as 1 Hence the value of expression is .

For any positive real number x, find the value of

${(\frac{x^{a}}{x^{b}})}^{a + b} \times {(\frac{x^{b}}{x^{c}})}^{b + c} \times {(\frac{x^{c}}{x^{a}})}^{c + a}$

We have to find the value of L =

By using rational exponents, we get

By using rational exponents we get

By definition we can write as 1

Hence the value of expression is .