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# Properties of Roots and Exponents Calculator

## The Properties of roots and exponents calculator is primarily intended to show how a particular property is implemented in practice. Each property has a description, a formula, and a definition area for numbers. To use the calculator, fill in the fields with the values on the right or left side of the expression. The calculator displays a detailed, expanded solution for each property.

 Property 1. To raise the number a to the power k/n - means to extract the root of the degree n from the number a to the power k. a â©¾ 0 n â©¾ 2, n âˆˆ N, N = {1, 2, 3...} k âˆˆ Z, Z = {-3, -2, -1, 0, 1, 2, 3...} =
 Property 2. The power of a number a with a negative exponent is one divided by the power of the same number with a positive exponent. a > 0 n âˆˆ R = 1
 Property 3. Extracting the root of degree n from the product of numbers a and b, can be represented as the product of the root of degree n from a, and the root of degree n from b. a â©¾ 0 b â©¾ 0 n â©¾ 2, n âˆˆ N, N = {1, 2, 3...} = â‹… â‹…
 Property 4. Extracting a root of degree n from a root of degree k of a, can be represented as a root of degree n by k of a. a â©¾ 0 n â©¾ 2, n âˆˆ N, N = {1, 2, 3...} k â©¾ 2, k âˆˆ N, N = {1, 2, 3...} = â‹…
 Property 5. The number a to the power of n + k, can be represented as the product of the numbers: a to the power of n and a to the power of k. a â©¾ 0, a âˆˆ R n âˆˆ Q k âˆˆ Q â‹… = +
 Property 6. The number a to the power of n-k, can be represented as the ratio of numbers: a to the power of n to a to the power of k. a â©¾ 0, a âˆˆ R n âˆˆ Q k âˆˆ Q : = âˆ’
 Property 7. When a number a is raised to the power of n to the power of k, he base of a remains the same, and the exponents of k and n are multiplied. a â©¾ 0, a âˆˆ R n âˆˆ Q k âˆˆ Q = â‹…
 Property 8. The product of numbers a and b to the power of n, can be represented as the product of the number a to the power of n and the number b to the power of n. a â©¾ 0, a âˆˆ R b â©¾ 0, b âˆˆ R n âˆˆ Q â‹… = â‹…
 Property 9. The ratio of numbers a and b to the power of n, can be represented as the ratio of the number a to the power of n to the number b to the power of n. a â©¾ 0, a âˆˆ R b > 0, b âˆˆ R n âˆˆ Q : = :
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