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

Understand Exponent Rule: Understand the exponent rule for powers raised to powers. When we have a power raised to another power, we multiply the exponents. (a^m)^n = a^(m*n)Apply Rule to Calculation: Apply the exponent rule to (2^7)^6. We multiply the exponents 7 and 6. (2^7)^6 = 2^(7*6) = 2^42Choose Equivalent Expression: Choose the equivalent expression for (2^7)^6. From the calculation in Step 2, we have determined that (2^7)^6 is equivalent to 2^42.

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Which expression is equivalent to $(2^7)^6$ ? $\newline$ Choices: $\newline$ (A) $2^{13}$ $\newline$ (B) $\frac{1}{2^{42}}$ $\newline$ (C) $\frac{1}{2^{13}}$ $\newline$ (D) $2^{42}$

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Math Problems

Algebra 1

Identify equivalent exponential expressions I

Full solution

Q. Which expression is equivalent to

(2^7)^6

\newline

Choices:

\newline

(A)

2^{13}

\newline

(B)

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

\newline

(C)

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

\newline

(D)

2^{42}

Understand Exponent Rule: Understand the exponent rule for powers raised to powers. $\newline$ When we have a power raised to another power, we multiply the exponents. $\newline$ $(a^m)^n = a^{(m*n)}$
Apply Rule to Calculation: Apply the exponent rule to $(2^7)^6$ . We multiply the exponents $7$ and $6$ . $(2^7)^6 = 2^{(7*6)} = 2^{42}$
Choose Equivalent Expression: Choose the equivalent expression for $(2^7)^6$ . From the calculation in Step $2$ , we have determined that $(2^7)^6$ is equivalent to $2^{42}$ .