Which expression is equivalent to (2^(-4))/((2^(2))^(4))? (1)/(2^(10)) (1)/(2^(14)) (1)/(2^(12)) 2^(12)

Simplify Denominator: Simplify the denominator. The denominator is (2^(2))^(4), which is a power of a power. According to the rules of exponents, when you raise a power to a power, you multiply the exponents. (2^(2))^(4) = 2^(2*4) = 2^(8)Rewrite Expression: Rewrite the original expression with the simplified denominator. Now we have the expression (2^(-4))/(2^(8)).Apply Quotient Rule: Apply the quotient rule for exponents. When dividing like bases with exponents, you subtract the exponents. 2^(-4) / 2^(8) = 2^(-4 - 8) = 2^(-12)Convert Negative Exponent: Convert the negative exponent to a positive exponent. A negative exponent means that the base is on the wrong side of the fraction line. To make the exponent positive, we can rewrite the expression as 1 over the base raised to the positive exponent. 2^(-12) = 1/(2^(12))Compare with Options: Compare the result with the given options. The expression 1/(2^(12)) matches one of the given options, which is (1)/(2^(12)).

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Which expression is equivalent to
(2^(-4))/((2^(2))^(4))?

(1)/(2^(10))

(1)/(2^(14))

(1)/(2^(12))

2^(12)

Which expression is equivalent to $\frac{2^{-4}}{\left(2^{2}\right)^{4}} ?$ $\newline$ $\frac{1}{2^{10}}$ $\newline$ $\frac{1}{2^{14}}$ $\newline$ $\frac{1}{2^{12}}$ $\newline$ $2^{12}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Which expression is equivalent to

\frac{2^{-4}}{\left(2^{2}\right)^{4}} ?

\newline

\frac{1}{2^{10}}

\newline

\frac{1}{2^{14}}

\newline

\frac{1}{2^{12}}

\newline

2^{12}

Simplify Denominator: Simplify the denominator. $\newline$ The denominator is $(2^{2})^{4}$ , which is a power of a power. According to the rules of exponents, when you raise a power to a power, you multiply the exponents. $\newline$ $(2^{2})^{4} = 2^{2\times4} = 2^{8}$
Rewrite Expression: Rewrite the original expression with the simplified denominator. $\newline$ Now we have the expression $(2^{-4})/(2^{8})$ .
Apply Quotient Rule: Apply the quotient rule for exponents. $\newline$ When dividing like bases with exponents, you subtract the exponents. $\newline$ $2^{-4} / 2^{8} = 2^{-4 - 8} = 2^{-12}$
Convert Negative Exponent: Convert the negative exponent to a positive exponent. $\newline$ A negative exponent means that the base is on the wrong side of the fraction line. To make the exponent positive, we can rewrite the expression as $1$ over the base raised to the positive exponent. $\newline$ $2^{-12} = \frac{1}{2^{12}}$
Compare with Options: Compare the result with the given options. $\newline$ The expression $\frac{1}{2^{12}}$ matches one of the given options, which is $\frac{1}{2^{12}}$ .