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Solve for [tex]\( x \)[/tex]:
[tex]\[ 3x = 6x - 2 \][/tex]

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[tex]$\left( x^3 \right)^5$[/tex] is equivalent to which expression?

A. [tex]\( x^{15} \)[/tex]

B. [tex]\( x^{8} \)[/tex]

C. [tex]\( x^{20} \)[/tex]

D. [tex]\( x^{35} \)[/tex]



Answer :

To determine the expression that [tex]\(\left(x^3\right)^5\)[/tex] is equivalent to, we use the power rule of exponents. The power rule of exponents states that [tex]\((a^m)^n = a^{m \cdot n}\)[/tex].

Let's break it down step-by-step:

1. Identify the base and the exponents: In the expression [tex]\(\left(x^3\right)^5\)[/tex], the base is [tex]\(x\)[/tex], the inner exponent is 3, and the outer exponent is 5.

2. Apply the power rule: Multiply the inner exponent by the outer exponent. So you would calculate [tex]\(3 \cdot 5\)[/tex].

3. Result of multiplication: [tex]\(3 \cdot 5 = 15\)[/tex].

4. Rewrite the expression: Substitute the new exponent back into the expression. [tex]\(\left(x^3\right)^5\)[/tex] becomes [tex]\(x^{15}\)[/tex].

Therefore, [tex]\(\left(x^3\right)^5\)[/tex] is equivalent to [tex]\(x^{15}\)[/tex].