Question

If a^m^n = (a^m)^n then the value of m in the terms of n is​

Answer 1

QUESTION:

If $\sf { {a}^{m} }^{n} = { ({a}^{m} })^{n}$, then find the value of m in terms of n

ANSWER:

• $\sf m=\sqrt[n]{mn}$

GIVEN:

• The value of m in terms of n is $\sf { {a}^{m} }^{n} = { ({a}^{m} })^{n}$

TO FIND:

• The value of m in terms of n.

EXPLANATION:

$\sf { {a}^{m} }^{n} = { ({a}^{m} })^{n}$

$\sf { {a}^{m} }^{n} = {a}^{mn}$

As the bases are same equate the powers.

$\sf {m}^n={mn}$

$\boxed{\bold{\gray{when \ x^y =z,\ x = \sqrt[y]{z}}}}$

$\sf m=\sqrt[n]{mn}$

Some other formulas:

$\boxed{\bold{\red{\large{\dfrac{x^m}{x^n}=x^{m-n}}}}}$

$\boxed{\bold{\blue{\large{{x^m}{x^n}=x^{m+n}}}}}$

$\boxed{\bold{\green{\large{(A+B)^2=A^2 + 2AB + B^2}}}}$

$\boxed{\bold{\orange{\large{(A-B)^2=A^2 -2AB + B^2}}}}$

$\boxed{\bold{\pink{\large{A^2+B^2=(A+B)^2-2AB}}}}$

$\boxed{\bold{\purple{\large{A^2-B^2=(A+B)(A-B)}}}}$

Answer 2

$\mathcal \red {{ \odot \_ \odot\: ANSWER:-}} </strong></p><p></p><p>\\ \\</p><p></p><p><strong>[tex] \sf { {a}^{m} }^{n} = ({a}^{m})^n \\ \\ \sf { {a}^{m} }^{n} = {a}^{mn} \\ \\ \sf \therefore \: {m}^{n} = mn \\ \\ \sf m = \sqrt[n]{mn}$