Question

Describe the error at the right. $$5 x^{-3}=\frac{1}{5 x^{3}}$$

   Describe the error at the right.
$$5 x^{-3}=\frac{1}{5 x^{3}}$$

Algebra 1

Ron Larson, Laurie… 1st Edition

Chapter 8, Problem 2

Instant Answer

Solved by Expert Amy Jiang

08/29/2020

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This is because any number raised to the power of -n is equal to 1 divided by that number raised to the power of n. Show more…

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Describe the error at the right. $$5 x^{-3}=\frac{1}{5 x^{3}}$$

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Key Concepts

Negative Exponent Rule

This rule states that any nonzero number raised to a negative exponent equals the reciprocal of that number raised to the corresponding positive exponent. For example, x?³ should be rewritten as 1/x³, indicating that the negative exponent inverts only the variable part of the term.

Multiplicative Coefficient Handling

When applying exponent rules, it is important to treat the multiplicative constant separately from the variable part that is being affected by the exponent. The constant remains unchanged; it should not be included in the inversion process dictated by the negative exponent.

Algebraic Manipulation Errors

Errors in rewriting expressions often occur when exponent rules are misapplied, such as inappropriately distributing the negative exponent to the constant as well as the variable. In this case, the mistake is in converting 5x?³ into 1/(5x³) instead of the correct 5/(x³), highlighting the importance of managing both coefficients and exponents correctly.

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