step 1 Hello, so you have seven to the third, divided by seven to the fourth, just going to be equal to

(-7 f^4)^2 | Numerade

Name: Problem 34, Chapter 5: Elementary Algebra
Uploaded: 2022-02-07T01:44:51-08:00
Duration: 12 s
Channel: Nick Johnson
Description: (-7 f^4)^2

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Key Concepts

Power of a Product Rule

When you raise a product of factors to an exponent, you apply the exponent to each factor individually. In algebra, this rule states that (ab)^n is equivalent to a^n multiplied by b^n, allowing complex expressions inside parentheses to be simplified by distributing the exponent across each term.

Exponentiation of Variables

In expressions involving variables and exponents, when an exponent is applied to a variable that is already raised to an exponent, the exponents are multiplied together. This rule, expressed as (x^m)^n = x^(m*n), is fundamental when simplifying expressions with stacked powers, ensuring that the variable’s exponent becomes the product of the original and the outer exponent.

Handling Negative Bases

When a negative base is raised to an exponent, the sign of the result depends on whether the exponent is even or odd. An even exponent results in a positive value because the negative factors cancel each other out in pairs, whereas an odd exponent preserves the negative sign. Understanding this property is crucial when simplifying expressions that include negative numbers with exponents.

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