Which expression is equivalent to (2^7)^6? Choices: (A)1/2^42 (B)2^42 (C)2^13 (D)1/2^13

Understand Exponent Rule: Understand the exponent rule for powers raised to powers. When a power is raised to another power, we multiply the exponents. (2^7)^6 = 2^(7*6)Calculate New Exponent: Calculate the new exponent. Multiply the exponents 7 and 6 to find the equivalent expression. 2^(7*6) = 2^42Match Result with Choices: Match the result with the given choices. The calculation from Step 2 gives us 2^42, which corresponds to choice (B).

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Math Problems

Grade 8

Identify equivalent expressions involving exponents I

Full solution

Q. Which expression is equivalent to

(2^7)^6

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Choices:

\newline

(A)

\frac{1}{2^{42}}

\newline

(B)

2^{42}

\newline

(C)

2^{13}

\newline

(D)

\frac{1}{2^{13}}

Understand Exponent Rule: Understand the exponent rule for powers raised to powers. $\newline$ When a power is raised to another power, we multiply the exponents. $\newline$ $(2^7)^6 = 2^{(7\times6)}$
Calculate New Exponent: Calculate the new exponent. $\newline$ Multiply the exponents $7$ and $6$ to find the equivalent expression. $\newline$ $2^{(7*6)} = 2^{42}$
Match Result with Choices: Match the result with the given choices. $\newline$ The calculation from Step $2$ gives us $2^{42}$ , which corresponds to choice (B).