Which expression is equivalent to (4^(-4))/(4^(5))×4^(-4) ? 4^(36) 16^(36) (1)/(16^(13)) (1)/(4^(13))

Simplify Expression: Simplify the expression using the properties of exponents. We have the expression (4^(-4))/(4^(5))×4^(-4). According to the properties of exponents, when we divide two expressions with the same base, we subtract the exponents. When we multiply two expressions with the same base, we add the exponents.Apply Exponent Rule: Apply the exponent subtraction rule to the division part of the expression. (4^(-4))/(4^(5)) = 4^(-4 - 5) = 4^(-9)Multiply Expressions: Now multiply the result from Step 2 by 4^(-4) using the exponent addition rule. 4^(-9) × 4^(-4) = 4^(-9 + -4) = 4^(-13)Rewrite in Familiar Form: Rewrite the expression in a more familiar form. 4^(-13) is equivalent to 1/(4^(13)), because a negative exponent indicates the reciprocal of the base raised to the positive exponent.Check Answer Choices: Check if any of the answer choices match the simplified expression. The expression 1/(4^(13)) is equivalent to the answer choice (1)/(4^(13)). None of the other choices match this expression.

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Which expression is equivalent to
(4^(-4))/(4^(5))×4^(-4) ?

4^(36)

16^(36)

(1)/(16^(13))

(1)/(4^(13))

Which expression is equivalent to $\frac{4^{-4}}{4^{5}} \times 4^{-4}$ ? $\newline$ $4^{36}$ $\newline$ $16^{36}$ $\newline$ $\frac{1}{16^{13}}$ $\newline$ $\frac{1}{4^{13}}$

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Math Problems

Algebra 1

Multiplication with rational exponents

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Q. Which expression is equivalent to

\frac{4^{-4}}{4^{5}} \times 4^{-4}

\newline

4^{36}

\newline

16^{36}

\newline

\frac{1}{16^{13}}

\newline

\frac{1}{4^{13}}

Simplify Expression: Simplify the expression using the properties of exponents. $\newline$ We have the expression $(4^{-4})/(4^{5})\times4^{-4}$ . According to the properties of exponents, when we divide two expressions with the same base, we subtract the exponents. When we multiply two expressions with the same base, we add the exponents.
Apply Exponent Rule: Apply the exponent subtraction rule to the division part of the expression. $\newline$ $(4^{-4})/(4^{5}) = 4^{-4 - 5} = 4^{-9}$
Multiply Expressions: Now multiply the result from Step $2$ by $4^{-4}$ using the exponent addition rule. $\newline$ $4^{-9} \times 4^{-4} = 4^{-9 + -4} = 4^{-13}$
Rewrite in Familiar Form: Rewrite the expression in a more familiar form. $4^{-13}$ is equivalent to $1/(4^{13})$ , because a negative exponent indicates the reciprocal of the base raised to the positive exponent.
Check Answer Choices: Check if any of the answer choices match the simplified expression. $\newline$ The expression $\frac{1}{4^{13}}$ is equivalent to the answer choice $\left(\frac{1}{4^{13}}\right)$ . None of the other choices match this expression.