Which expression is equivalent to ((2 x)^5)/(x^3) ? A) 2 x^2 B) 32 x^2 C) 2 x^8

step 1 which expression is equivalent to 2 to the power to x or to the power of 5 divided by x to the p

Which expression is equivalent to ((2 x)^5)/(x^3) ? A) ...

Which expression is equivalent to $\frac{(2 x)^{5}}{x^{3}} ?$
$$
\begin{array}{llll}{\text { A) } 2 x^{2}} & {\text { B) } 32 x^{2}} & {\text { C) } 2 x^{8}} & {\text { D) } 32 x^{-2}}\end{array}
$$

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Key Concepts

Laws of Exponents

Laws of exponents provide guidelines for performing operations on expressions with exponents. A key part of these laws is the quotient rule, which specifies that when dividing expressions with the same base, you subtract the exponents (i.e., a^m / a^n = a^(m–n)). This rule is crucial when simplifying expressions like x^5 / x^3.

Simplifying Rational Expressions

Simplifying rational expressions involves reducing complex expressions, usually through the application of the laws of exponents and cancellation of common factors in the numerator and denominator. This process involves systematically deconstructing the expression to its simplest form, which is an essential skill in algebra.

Power of a Product Rule

This rule states that when you have a product of factors raised to an exponent, you can apply the exponent to each factor individually. In generic terms, (ab)^n equals a^n multiplied by b^n, which is essential when breaking down expressions like (2x)^5 into 2^5 and x^5.

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