Which expression is equivalent to ((4^(-4))^(-5))/(4^(5))? 4^(-14) 4^(15) 4^(-25) 4^(17)

Understand and Apply Power Rule: Understand the problem and apply the power of a power rule. We have the expression ((4^(-4))^(-5))/(4^(5)). According to the power of a power rule, (a^m)^n = a^(m*n). We will apply this rule to the numerator.Apply Power of Power Rule: Apply the power of a power rule to the numerator. ((4^(-4))^(-5)) = 4^((-4)*(-5)) = 4^(20).Rewrite with Simplified Numerator: Rewrite the expression with the simplified numerator. Now the expression is 4^(20)/(4^(5)).Apply Quotient of Powers Rule: Apply the quotient of powers rule. According to the quotient of powers rule, a^(m)/a^(n) = a^(m-n). We will apply this rule to the expression.Subtract Exponents: Subtract the exponents. 4^(20)/(4^(5)) = 4^(20-5) = 4^(15).Check Answer Choices: Check the answer choices to see which one matches our result. The expression 4^(15) matches one of the answer choices, which is 4^(15).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

4^(-14)

4^(15)

4^(-25)

4^(17)

Which expression is equivalent to $\frac{\left(4^{-4}\right)^{-5}}{4^{5}} ?$ $\newline$ $4^{-14}$ $\newline$ $4^{15}$ $\newline$ $4^{-25}$ $\newline$ $4^{17}$

View step-by-step help

Home

Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Which expression is equivalent to

\frac{\left(4^{-4}\right)^{-5}}{4^{5}} ?

\newline

4^{-14}

\newline

4^{15}

\newline

4^{-25}

\newline

4^{17}

Understand and Apply Power Rule: Understand the problem and apply the power of a power rule. $\newline$ We have the expression $((4^{-4})^{-5})/(4^{5})$ . According to the power of a power rule, $(a^{m})^{n} = a^{m*n}$ . We will apply this rule to the numerator.
Apply Power of Power Rule: Apply the power of a power rule to the numerator. $\newline$ $((4^{-4})^{-5}) = 4^{(-4)(-5)} = 4^{20}$ .
Rewrite with Simplified Numerator: Rewrite the expression with the simplified numerator. $\newline$ Now the expression is $4^{20}/(4^{5})$ .
Apply Quotient of Powers Rule: Apply the quotient of powers rule. $\newline$ According to the quotient of powers rule, $a^{m}/a^{n} = a^{(m-n)}$ . We will apply this rule to the expression.
Subtract Exponents: Subtract the exponents. $4^{20}/(4^{5}) = 4^{20-5} = 4^{15}.$
Check Answer Choices: Check the answer choices to see which one matches our result. $\newline$ The expression $4^{15}$ matches one of the answer choices, which is $4^{15}$ .