Which expression is equivalent to (4×4^(-1))^(3) ? 16 1 (1)/(64) 0

Identify base and exponents: Identify the base and the exponents in the expression (4×4^(-1))^(3). We have a multiplication inside the parentheses followed by an exponentiation.Simplify inside parentheses: Simplify the expression inside the parentheses first, using the property of exponents that states a^(m) * a^(n) = a^(m+n). Here, we have 4^(1) * 4^(-1), which simplifies to 4^(1-1) = 4^(0).Recall power of 0: Recall that any non-zero number raised to the power of 0 is 1. Therefore, 4^(0) = 1.Raise to power of 3: Now raise the simplified expression inside the parentheses to the power of 3. (4×4^(-1))^(3) simplifies to 1^(3).Final result: Any number raised to the power of 3 is itself multiplied by itself three times. Since 1 multiplied by itself any number of times is still 1, 1^(3) = 1.

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Q. Which expression is equivalent to

\left(4 \times 4^{-1}\right)^{3}

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16

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1

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\frac{1}{64}

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0

Identify base and exponents: Identify the base and the exponents in the expression $(4\times4^{-1})^{3}$ . We have a multiplication inside the parentheses followed by an exponentiation.
Simplify inside parentheses: Simplify the expression inside the parentheses first, using the property of exponents that states $a^{m} \times a^{n} = a^{m+n}$ . Here, we have $4^{1} \times 4^{-1}$ , which simplifies to $4^{1-1} = 4^{0}$ .
Recall power of $0$ : Recall that any non-zero number raised to the power of $0$ is $1$ . $\newline$ Therefore, $4^{0} = 1$ .
Raise to power of $3$ : Now raise the simplified expression inside the parentheses to the power of $3$ . $(4\times4^{-1})^{3}$ simplifies to $1^{3}$ .
Final result: Any number raised to the power of $3$ is itself multiplied by itself three times. $\newline$ Since $1$ multiplied by itself any number of times is still $1$ , $1^{3} = 1$ .