Which expression is equivalent to (4^(3))/(4^(-7)*4^(7))? 16 (1)/(64) 64 4

Simplify Expression: Simplify the expression using the properties of exponents. We have the expression (4^(3))/(4^(-7)*4^(7)). According to the properties of exponents, when we divide powers with the same base, we subtract the exponents. When we multiply powers with the same base, we add the exponents.Apply Exponent Properties: Apply the properties of exponents to the denominator. First, we'll simplify the denominator by adding the exponents of the terms with the same base: 4^(-7) * 4^(7) = 4^(-7+7) = 4^(0) Since any number raised to the power of 0 is 1, we have: 4^(0) = 1Divide Numerator by Denominator: Divide the numerator by the denominator. Now we divide 4^(3) by 1, which is simply 4^(3) since any number divided by 1 is the number itself: (4^(3))/1 = 4^(3)Calculate 4^3: Calculate the value of 4^(3). 4^(3) means 4 multiplied by itself 3 times: 4^(3) = 4 * 4 * 4 = 64

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Which expression is equivalent to
(4^(3))/(4^(-7)*4^(7))?
16

(1)/(64)
64
4

Which expression is equivalent to $\frac{4^{3}}{4^{-7} \cdot 4^{7}} ?$ $\newline$ $16$ $\newline$ $\frac{1}{64}$ $\newline$ $64$ $\newline$ $4$

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Algebra 1

Multiplication with rational exponents

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Q. Which expression is equivalent to

\frac{4^{3}}{4^{-7} \cdot 4^{7}} ?

\newline

16

\newline

\frac{1}{64}

\newline

64

\newline

4

Simplify Expression: Simplify the expression using the properties of exponents. $\newline$ We have the expression $(4^{3})/(4^{-7}*4^{7})$ . According to the properties of exponents, when we divide powers with the same base, we subtract the exponents. When we multiply powers with the same base, we add the exponents.
Apply Exponent Properties: Apply the properties of exponents to the denominator. $\newline$ First, we'll simplify the denominator by adding the exponents of the terms with the same base: $\newline$ $4^{-7} \times 4^{7} = 4^{-7+7} = 4^{0}$ $\newline$ Since any number raised to the power of $0$ is $1$ , we have: $\newline$ $4^{0} = 1$
Divide Numerator by Denominator: Divide the numerator by the denominator. $\newline$ Now we divide $4^{3}$ by $1$ , which is simply $4^{3}$ since any number divided by $1$ is the number itself: $\newline$ $\frac{4^{3}}{1} = 4^{3}$
Calculate $4^3$ : Calculate the value of $4^{3}$ . $4^{3}$ means $4$ multiplied by itself $3$ times: $4^{3} = 4 \times 4 \times 4 = 64$