Which of the following is equivalent to (2x^(3)y^(4)z^(5))^(3) ? Choose 1 answer: (A) 6x^(9)y^(12)z^(15) (B) 8x^(9)y^(12)z^(15) (C) 6x^(6)y^(7)z^(8) (D) 8x^(6)y^(7)z^(8)

Apply power of power rule: Apply the power of a power rule. The power of a power rule states that (a^(m))^n = a^(m*n). We will apply this rule to each term inside the parentheses. (2x^(3)y^(4)z^(5))^(3) = 2^(3) * (x^(3))^(3) * (y^(4))^(3) * (z^(5))^(3)Calculate powers: Calculate the powers. Now we calculate each term separately: 2^(3) = 2 * 2 * 2 = 8 (x^(3))^(3) = x^(3*3) = x^(9) (y^(4))^(3) = y^(4*3) = y^(12) (z^(5))^(3) = z^(5*3) = z^(15)Combine the results: Combine the results. Combining the results from Step 2, we get: 8 * x^(9) * y^(12) * z^(15)Match with given options: Match the result with the given options. The result from Step 3 matches option (B): (B) 8x^(9)y^(12)z^(15)

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Which of the following is equivalent to
(2x^(3)y^(4)z^(5))^(3) ?
Choose 1 answer:
(A)
6x^(9)y^(12)z^(15)
(B)
8x^(9)y^(12)z^(15)
(C)
6x^(6)y^(7)z^(8)
(D)
8x^(6)y^(7)z^(8)

Which of the following is equivalent to $\left(2 x^{3} y^{4} z^{5}\right)^{3}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $6 x^{9} y^{12} z^{15}$ $\newline$ (B) $8 x^{9} y^{12} z^{15}$ $\newline$ (C) $6 x^{6} y^{7} z^{8}$ $\newline$ (D) $8 x^{6} y^{7} z^{8}$

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Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

Q. Which of the following is equivalent to

\left(2 x^{3} y^{4} z^{5}\right)^{3}

\newline

Choose

1

answer:

\newline

(A)

6 x^{9} y^{12} z^{15}

\newline

(B)

8 x^{9} y^{12} z^{15}

\newline

(C)

6 x^{6} y^{7} z^{8}

\newline

(D)

8 x^{6} y^{7} z^{8}

Apply power of power rule: Apply the power of a power rule. $\newline$ The power of a power rule states that $(a^{m})^{n} = a^{m*n}$ . We will apply this rule to each term inside the parentheses. $\newline$ $(2x^{3}y^{4}z^{5})^{3} = 2^{3} \times (x^{3})^{3} \times (y^{4})^{3} \times (z^{5})^{3}$
Calculate powers: Calculate the powers. $\newline$ Now we calculate each term separately: $\newline$ $2^{3} = 2 \times 2 \times 2 = 8$ $\newline$ $(x^{3})^{3} = x^{3\times3} = x^{9}$ $\newline$ $(y^{4})^{3} = y^{4\times3} = y^{12}$ $\newline$ $(z^{5})^{3} = z^{5\times3} = z^{15}$
Combine the results: Combine the results. $\newline$ Combining the results from Step $2$ , we get: $\newline$ $8 \cdot x^{9} \cdot y^{12} \cdot z^{15}$
Match with given options: Match the result with the given options. $\newline$ The result from Step $3$ matches option (B): $\newline$ (B) $8x^{9}y^{12}z^{15}$