Simplify: (2r^(5))^(3) Answer:

Apply Power Rule: To simplify the expression (2r^(5))^(3), we need to apply the power of a power rule, which states that (a^(m))^n = a^(m*n) for any real number a and integers m and n. Here, we have a = 2r^(5) and both m and n are equal to 3. Calculation: (2r^(5))^(3) = 2^(3) * (r^(5))^(3)Calculate 2^3: Now we simplify each part separately. First, we calculate 2^(3), which is 2 * 2 * 2. Calculation: 2^(3) = 8Apply Power Rule to r^5: Next, we apply the power of a power rule to r^(5) raised to the power of 3, which means we multiply the exponents. Calculation: (r^(5))^(3) = r^(5*3) = r^(15)Combine Results: Finally, we combine the results from the previous steps to get the final simplified expression. Calculation: 8 * r^(15)

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Algebra 2

Simplify variable expressions using properties

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Q. Simplify:

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\left(2 r^{5}\right)^{3}

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Answer:

Apply Power Rule: To simplify the expression $(2r^{5})^{3}$ , we need to apply the power of a power rule, which states that $(a^{m})^{n} = a^{m*n}$ for any real number $a$ and integers $m$ and $n$ . Here, we have $a = 2r^{5}$ and both $m$ and $n$ are equal to $3$ . $\newline$ Calculation: $(2r^{5})^{3} = 2^{3} \times (r^{5})^{3}$
Calculate $2^3$ : Now we simplify each part separately. First, we calculate $2^{3}$ , which is $2 \times 2 \times 2$ . $\newline$ Calculation: $2^{3} = 8$
Apply Power Rule to $r^5$ : Next, we apply the power of a power rule to $r^{(5)}$ raised to the power of $3$ , which means we multiply the exponents. $\newline$ Calculation: $(r^{(5)})^{(3)} = r^{(5*3)} = r^{(15)}$
Combine Results: Finally, we combine the results from the previous steps to get the final simplified expression. $\newline$ Calculation: $8 \times r^{15}$