Rewrite <math><mstyle displaystyle="true"><msup><mrow><mroot><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></mroot></mrow><mrow><mi>n</mi></mrow></msup></mstyle></math> as <math><mstyle displaystyle="true"><mi>a</mi></mstyle></math> .

Use <math><mstyle displaystyle="true"><mroot><mrow><msup><mrow><mi>a</mi></mrow><mrow><mi>x</mi></mrow></msup></mrow><mrow><mi>n</mi></mrow></mroot><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mfrac><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msup></mstyle></math> to rewrite <math><mstyle displaystyle="true"><mroot><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></mroot></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msup></mstyle></math> .

Apply the power rule and multiply exponents, <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>)</mo></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mi>n</mi></mrow></msup></mstyle></math> .

Combine <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mi>n</mi></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mi>n</mi></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mi>n</mi></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Simplify.

Since the two sides have been shown to be equivalent, the equation is an identity.

Do you know how to Verify the Identity (n root of a)^n=a? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Name | seven hundred sixty-four million five hundred thousand three hundred seventy-six |
---|

- 764500376 has 64 divisors, whose sum is
**2606764032** - The reverse of 764500376 is
**673005467** - Previous prime number is
**647**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 38
- Digital Root 2

Name | one billion nine hundred seven million six hundred twenty-four thousand six hundred sixty-six |
---|

- 1907624666 has 4 divisors, whose sum is
**2861437002** - The reverse of 1907624666 is
**6664267091** - Previous prime number is
**2**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 47
- Digital Root 2

Name | nine hundred seventy million four hundred eighty-nine thousand three hundred twelve |
---|

- 970489312 has 256 divisors, whose sum is
**7981500240** - The reverse of 970489312 is
**213984079** - Previous prime number is
**179**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 43
- Digital Root 7