(2b^(-5))^(3) Which of the following is equivalent to the given expression for all b!=0 ? Choose 1 answer: (A) (2)/(b^(15)) (B) (8)/(b^(15)) (c) (1)/(2b^(15)) (D) (1)/(8b^(15))

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 the given expression (2b^(-5))^3. (2b^(-5))^3 = 2^3 * (b^(-5))^3Calculate powers: Calculate the powers. Now we calculate the powers separately for 2^3 and (b^(-5))^3. 2^3 = 2 * 2 * 2 = 8 (b^(-5))^3 = b^(-5*3) = b^(-15)Combine results: Combine the results. We combine the results from Step 2 to get the final expression. (2b^(-5))^3 = 8 * b^(-15)Write expression with positive exponent: Write the expression with positive exponent. Since b^(-15) means 1/(b^15), we rewrite the expression with a positive exponent. 8 * b^(-15) = 8 / (b^15)Match result with given choices: Match the result with the given choices. The expression we found is 8 / (b^15), which matches choice (B).

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(2b^(-5))^(3)
Which of the following is equivalent to the given expression for all
b!=0 ?
Choose 1 answer:
(A)
(2)/(b^(15))
(B)
(8)/(b^(15))
(c)
(1)/(2b^(15))
(D)
(1)/(8b^(15))

$\left(2 b^{-5}\right)^{3}$ $\newline$ Which of the following is equivalent to the given expression for all $b \neq 0$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{2}{b^{15}}$ $\newline$ (B) $\frac{8}{b^{15}}$ $\newline$ (C) $\frac{1}{2 b^{15}}$ $\newline$ (D) $\frac{1}{8 b^{15}}$

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Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

\left(2 b^{-5}\right)^{3}

\newline

Which of the following is equivalent to the given expression for all

b \neq 0

\newline

Choose

1

answer:

\newline

(A)

\frac{2}{b^{15}}

\newline

(B)

\frac{8}{b^{15}}

\newline

(C)

\frac{1}{2 b^{15}}

\newline

(D)

\frac{1}{8 b^{15}}

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 the given expression $(2b^{-5})^3$ . $\newline$ $(2b^{-5})^3 = 2^3 \cdot (b^{-5})^3$
Calculate powers: Calculate the powers. $\newline$ Now we calculate the powers separately for $2^3$ and $(b^{-5})^3$ . $\newline$ $2^3 = 2 \times 2 \times 2 = 8$ $\newline$ $(b^{-5})^3 = b^{-5 \times 3} = b^{-15}$
Combine results: Combine the results. $\newline$ We combine the results from Step $2$ to get the final expression. $\newline$ $(2b^{-5})^3 = 8 \cdot b^{-15}$
Write expression with positive exponent: Write the expression with positive exponent. $\newline$ Since $b^{-15}$ means $1/(b^{15})$ , we rewrite the expression with a positive exponent. $\newline$ $8 \cdot b^{-15} = 8 / (b^{15})$
Match result with given choices: Match the result with the given choices. $\newline$ The expression we found is $\frac{8}{b^{15}}$ , which matches choice (B).