Which of the following is equivalent to (2^(x))^(3) ? Choose 1 answer: (A) 6^(x) (B) 6^(x^(3)) (C) 8^(x) (D) 8^(3x)

Simplify expression using laws of exponents: We need to simplify the expression (2^(x))^(3) using the laws of exponents. According to the laws of exponents, (a^(m))^n = a^(m*n). So, (2^(x))^(3) = 2^(x*3).Perform multiplication inside the exponent: Now we perform the multiplication inside the exponent. x*3 = 3x. So, 2^(x*3) = 2^(3x).Compare simplified expression with given choices: We compare the simplified expression with the given choices. 2^(3x) matches with choice (D) 8^(3x). However, we need to verify if 2^(3x) is indeed equal to 8^(3x). We know that 8 is 2 raised to the power of 3, i.e., 8 = 2^3. So, 2^(3x) is not equal to 8^(3x) because 8^(3x) would imply (2^3)^(3x), which is not the same as 2^(3x).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Which of the following is equivalent to
(2^(x))^(3) ?
Choose 1 answer:
(A)
6^(x)
(B)
6^(x^(3))
(C)
8^(x)
(D)
8^(3x)

Which of the following is equivalent to $\left(2^{x}\right)^{3}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $6^{x}$ $\newline$ (B) $6^{x^{3}}$ $\newline$ (C) $8^{x}$ $\newline$ (D) $8^{3 x}$

View step-by-step help

Home

Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

Q. Which of the following is equivalent to

\left(2^{x}\right)^{3}

\newline

Choose

1

answer:

\newline

(A)

6^{x}

\newline

(B)

6^{x^{3}}

\newline

(C)

8^{x}

\newline

(D)

8^{3 x}

Simplify expression using laws of exponents: We need to simplify the expression $(2^{x})^{3}$ using the laws of exponents. $\newline$ According to the laws of exponents, $(a^{m})^{n} = a^{m*n}$ . $\newline$ So, $(2^{x})^{3} = 2^{x*3}$ .
Perform multiplication inside the exponent: Now we perform the multiplication inside the exponent. $\newline$ $x \times 3 = 3x$ . $\newline$ So, $2^{(x \times 3)} = 2^{3x}$ .
Compare simplified expression with given choices: We compare the simplified expression with the given choices. $\newline$ $2^{3x}$ matches with choice (D) $8^{3x}$ . $\newline$ However, we need to verify if $2^{3x}$ is indeed equal to $8^{3x}$ . $\newline$ We know that $8$ is $2$ raised to the power of $3$ , i.e., $8 = 2^3$ . $\newline$ So, $2^{3x}$ is not equal to $8^{3x}$ because $8^{3x}$ would imply $8^{3x}$ $1$ , which is not the same as $2^{3x}$ .