Question

Представьте 36a⁶b¹² в виде степени произведения​

Answer 1

$36a^{6} b^{12} = (6a^{3} b^{6})^{2}$

Answer 2

Ответ:

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36a^6b^12 = (6a^3b^6)^2

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Answer 3

Expressing 36a⁶b¹² as a Power of a Product

To express the expression 36a⁶b¹² as a power of a product, we can break down 36 into its prime factors and then rewrite the expression accordingly.

Prime Factorization of 36

The prime factorization of 36 is: 36 = 2² * 3²

Rewriting 36a⁶b¹²

Now, we can express 36a⁶b¹² as a power of a product using the prime factorization of 36: 36a⁶b¹² = (2² * 3²)a⁶b¹²

Expressing as a Power of a Product

We can further simplify this expression by using the properties of exponents: (2² * 3²)a⁶b¹² = (2²a³)² * (3²b⁶)

Therefore, 36a⁶b¹² can be expressed as (2²a³)² * (3²b⁶) in the form of a power of a product.