Apply Quotient Rule: Apply the quotient rule for exponents which states that $a^m/a^n = a^{m-n}$ when $a$ is a non-zero number. $4^{11}/4^{-8} = 4^{11 - (-8)}$ $4^{11}/4^{-8} = 4^{11 + 8}$ $4^{11}/4^{-8} = 4^{19}$Calculate Value: Calculate the value of $4^{19}$. Since this is a large number, we can express it in terms of powers of 2 because $4 = 2^2$. $4^{19} = (2^2)^{19}$ $4^{19} = 2^{2 \times 19}$ $4^{19} = 2^{38}$Recognize Simplified Form: Recognize that calculating $2^{38}$ is not practical without a calculator and is not necessary for the problem. The problem asks for the expression in simplified form, not the actual numerical value. Therefore, the simplified form of $4^{11}/4^{-8}$ is $2^{38}$.

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$\dfrac{4^{11}}{4^{-8}}=\Box$

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Math Problems

Algebra 2

Csc, sec, and cot of special angles

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\dfrac{4^{11}}{4^{-8}}=\Box

Apply Quotient Rule: Apply the quotient rule for exponents which states that $a^m/a^n = a^{m-n}$ when $a$ is a non-zero number. $\newline$ $4^{11}/4^{-8} = 4^{11 - (-8)}$ $\newline$ $4^{11}/4^{-8} = 4^{11 + 8}$ $\newline$ $4^{11}/4^{-8} = 4^{19}$
Calculate Value: Calculate the value of $4^{19}$ . Since this is a large number, we can express it in terms of powers of $2$ because $4 = 2^2$ . $\newline$ $4^{19} = (2^2)^{19}$ $\newline$ $4^{19} = 2^{2 \times 19}$ $\newline$ $4^{19} = 2^{38}$
Recognize Simplified Form: Recognize that calculating $2^{38}$ is not practical without a calculator and is not necessary for the problem. The problem asks for the expression in simplified form, not the actual numerical value. Therefore, the simplified form of $4^{11}/4^{-8}$ is $2^{38}$ .