Which expressions are equivalent to (d^((1)/(8)))^(5) ? Choose all answers that apply: A. (d^(5))^((1)/(8)) B (d^(5))^(8) C (root(8)(d))^(5) D None of the above

Understanding Exponent Properties: Understand the properties of exponents. When raising a power to a power, you multiply the exponents. This is based on the property (a^m)^n = a^(m*n).Applying Exponent Property to the Expression: Apply the exponent property to the given expression. (d^(1/8))^5 = d^((1/8)*5) = d^(5/8)Checking Answer Choice A: Check each answer choice to see if it is equivalent to d^(5/8). A. (d^5)^(1/8) = d^(5*(1/8)) = d^(5/8) This matches our expression from Step 2, so choice A is equivalent.Checking Answer Choice B: Check choice B. B. (d^5)^8 = d^(5*8) = d^40 This does not match our expression from Step 2, so choice B is not equivalent.Checking Answer Choice C: Check choice C. C. (root(8)(d))^5 = (d^(1/8))^5 = d^(5/8) This matches our expression from Step 2, so choice C is equivalent.Checking Answer Choice D: Check choice D. D. None of the above Since we have found that choices A and C are equivalent to the given expression, choice D is not correct.

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Which expressions are equivalent to
(d^((1)/(8)))^(5) ?
Choose all answers that apply:
A.
(d^(5))^((1)/(8))
B
(d^(5))^(8)
C
(root(8)(d))^(5)
D None of the above

Which expressions are equivalent to $\left(d^{\frac{1}{8}}\right)^{5}$ ? $\newline$ Choose all answers that apply: $\newline$ A. $\left(d^{5}\right)^{\frac{1}{8}}$ $\newline$ B $\left(d^{5}\right)^{8}$ $\newline$ C $(\sqrt[8]{d})^{5}$ $\newline$ D None of the above

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Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

Q. Which expressions are equivalent to

\left(d^{\frac{1}{8}}\right)^{5}

\newline

Choose all answers that apply:

\newline

\left(d^{5}\right)^{\frac{1}{8}}

\newline

\left(d^{5}\right)^{8}

\newline

(\sqrt[8]{d})^{5}

\newline

D None of the above

Understanding Exponent Properties: Understand the properties of exponents. When raising a power to a power, you multiply the exponents. This is based on the property $(a^m)^n = a^{m*n}$ .
Applying Exponent Property to the Expression: Apply the exponent property to the given expression. $\newline$ $(d^{\frac{1}{8}})^5 = d^{(\frac{1}{8}\cdot5)} = d^{\frac{5}{8}}$
Checking Answer Choice A: Check each answer choice to see if it is equivalent to $d^{5/8}$ .
A. $(d^5)^{1/8} = d^{5*(1/8)} = d^{5/8}$
This matches our expression from Step $2$ , so choice A is equivalent.
Checking Answer Choice B: Check choice B. $\newline$ B. $(d^5)^8 = d^{(5\times8)} = d^{40}$ $\newline$ This does not match our expression from Step $2$ , so choice B is not equivalent.
Checking Answer Choice C: Check choice C. $\newline$ C. $(\sqrt[8]{d})^5 = (d^{1/8})^5 = d^{5/8}$ $\newline$ This matches our expression from Step $2$ , so choice C is equivalent.
Checking Answer Choice D: Check choice D. $\newline$ D. None of the above $\newline$ Since we have found that choices A and C are equivalent to the given expression, choice D is not correct.