Question

25 numeric 1 point
solve for x: \\(\frac{1}{2}(5x - 8) = 26\\)
answer

26 multiple choice 1 point
simplify \\((x^6)^3\\)
\\(3x^6\\)
\\(6x^3\\)
\\(x^{18}\\)
\\(x^9\\)

27 multiple answer 1 point
which expression(s) are equivalent to \\(x^{18}\\) (mark all that apply)
\\(\frac{x^{36}}{x^2}\\)
\\(x^3x^6\\)
\\(\frac{x^{20}}{x^2}\\)
\\((x^3)^6\\)
\\(x^7x^{11}\\)
\\(\frac{x^{19}}{x}\\)
\\(x^9x^2\\)

Explanation:

Question 25

Step1: Eliminate the fraction

Multiply both sides by 2:
$$2 \times \frac{1}{2}(5x - 8) = 26 \times 2$$
$$5x - 8 = 52$$

Step2: Isolate the term with x

Add 8 to both sides:
$$5x - 8 + 8 = 52 + 8$$
$$5x = 60$$

Step3: Solve for x

Divide both sides by 5:
$$\frac{5x}{5} = \frac{60}{5}$$
$$x = 12$$

Step1: Apply exponent power rule

Use $(a^m)^n = a^{m \times n}$:
$$(x^6)^3 = x^{6 \times 3} = x^{18}$$

Evaluate each option using exponent rules:

1. $\frac{x^{20}}{x^2} = x^{20-2} = x^{18}$ (matches)
2. $x^3x^6 = x^{3+6} = x^9$ (does not match)
3. $\frac{x^{20}}{x^3} = x^{20-3} = x^{17}$ (does not match)
4. $(x^3)^6 = x^{3 \times 6} = x^{18}$ (matches)
5. $x^7x^{11} = x^{7+11} = x^{18}$ (matches)
6. $\frac{x^{19}}{x} = x^{19-1} = x^{18}$ (matches)
7. $x^9x^2 = x^{9+2} = x^{11}$ (does not match)

Answer:

$12$

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Question 26