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(x^((7)/(4))*x^(4))^(4)
Which of the following expressions is equivalent to the given expression assuming
x is nonzero?
Choose 1 answer:
(A)
x^((39)/(4))
(B)
x^(11)
(C)
x^(23)
(D)
x^(28)

$\left(x^{\frac{7}{4}} \cdot x^{4}\right)^{4}$ $\newline$ Which of the following expressions is equivalent to the given expression assuming $x$ is nonzero? $\newline$ Choose $1$ answer: $\newline$ (A) $x \frac{39}{4}$ $\newline$ (B) $x^{11}$ $\newline$ (C) $x^{23}$ $\newline$ (D) $x^{28}$

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Compare linear and exponential growth

Full solution

Q.

\left(x^{\frac{7}{4}} \cdot x^{4}\right)^{4}

\newline

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

x

is nonzero?

\newline

Choose

1

answer:

\newline

(A)

x \frac{39}{4}

\newline

(B)

x^{11}

\newline

(C)

x^{23}

\newline

(D)

x^{28}

Simplify inside the parentheses: First, let's simplify the inside of the parentheses by using the property of exponents that states when you multiply powers with the same base, you add the exponents. $\newline$ The expression inside the parentheses is $x^{\left(\frac{7}{4}\right)} \cdot x^{4}$ . $\newline$ We add the exponents: $\left(\frac{7}{4}\right) + 4$ . $\newline$ Since $4$ can be written as $\frac{16}{4}$ , we have $\left(\frac{7}{4}\right) + \left(\frac{16}{4}\right) = \left(\frac{23}{4}\right)$ . $\newline$ So, the expression inside the parentheses simplifies to $x^{\left(\frac{23}{4}\right)}$ .
Apply the exponent outside the parentheses: Now, we need to apply the exponent outside the parentheses, which is $4$ , to the simplified expression inside the parentheses. $\newline$ Using the property of exponents that states when you raise a power to a power, you multiply the exponents, we have $(x^{(\frac{23}{4})})^4$ . $\newline$ We multiply the exponents: $(\frac{23}{4}) \cdot 4$ . $\newline$ The $4$ s cancel out, leaving us with $23 \cdot 1 = 23$ . $\newline$ So, the expression simplifies to $x^{23}$ .
Compare with answer choices: We can now compare the simplified expression to the answer choices. $\newline$ The expression we found is $x^{23}$ , which matches answer choice (C).

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