(2y^(2)z^(10))^(5) Which of the following expressions is equivalent to the given expression? Choose 1 answer: (A) 10y^(32)z^(100,000) (B) 10y^(10)z^(50) (C) 32y^(32)z^(100,000) (D) 32y^(10)z^(50)

Apply power of power rule: Apply the power of a power rule to the given expression. The power of a power rule states that (a^(m))^n = a^(m*n). We apply this rule to each part of the expression separately. (2y^(2)z^(10))^(5) = 2^(5) * (y^(2))^5 * (z^(10))^5Calculate each part: Calculate each part of the expression using the power of a power rule. 2^(5) = 32 (y^(2))^5 = y^(2*5) = y^(10) (z^(10))^5 = z^(10*5) = z^(50)Combine the results: Combine the results to get the final expression. The final expression is 32 * y^(10) * z^(50).Match with given choices: Match the final expression with the given choices. The final expression 32 * y^(10) * z^(50) matches with choice (D).

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(2y^(2)z^(10))^(5)
Which of the following expressions is equivalent to the given expression?
Choose 1 answer:
(A)
10y^(32)z^(100,000)
(B)
10y^(10)z^(50)
(C)
32y^(32)z^(100,000)
(D)
32y^(10)z^(50)

$\left(2 y^{2} z^{10}\right)^{5}$ $\newline$ Which of the following expressions is equivalent to the given expression? $\newline$ Choose $1$ answer: $\newline$ (A) $10 y^{32} z^{100,000}$ $\newline$ (B) $10 y^{10} z^{50}$ $\newline$ (C) $32 y^{32} z^{100,000}$ $\newline$ (D) $32 y^{10} z^{50}$

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Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

\left(2 y^{2} z^{10}\right)^{5}

\newline

Which of the following expressions is equivalent to the given expression?

\newline

Choose

1

answer:

\newline

(A)

10 y^{32} z^{100,000}

\newline

(B)

10 y^{10} z^{50}

\newline

(C)

32 y^{32} z^{100,000}

\newline

(D)

32 y^{10} z^{50}

Apply power of power rule: Apply the power of a power rule to the given expression. $\newline$ The power of a power rule states that $(a^{m})^{n} = a^{m*n}$ . We apply this rule to each part of the expression separately. $\newline$ $(2y^{2}z^{10})^{5} = 2^{5} \cdot (y^{2})^{5} \cdot (z^{10})^{5}$
Calculate each part: Calculate each part of the expression using the power of a power rule. $\newline$ $2^{5} = 32$ $\newline$ $(y^{2})^{5} = y^{2\cdot5} = y^{10}$ $\newline$ $(z^{10})^{5} = z^{10\cdot5} = z^{50}$
Combine the results: Combine the results to get the final expression. $\newline$ The final expression is $32 \cdot y^{10} \cdot z^{50}$ .
Match with given choices: Match the final expression with the given choices. $\newline$ The final expression $32 \cdot y^{10} \cdot z^{50}$ matches with choice (D).