Select the equivalent expression. (x^(-7))/(x^(-6)*x^(4)) x^(9) (1)/(x^(5)) (1)/(x^(9)) x^(5)

Simplify Expression: Simplify the expression using the properties of exponents. We have the expression (x^(-7))/(x^(-6)*x^(4)). 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 Properties: Apply the properties of exponents to the denominator. First, we will simplify the denominator by adding the exponents of x since they are being multiplied together. x^(-6)*x^(4) = x^(-6+4) = x^(-2)Divide Numerator: Now, divide the numerator by the simplified denominator. We have x^(-7) divided by x^(-2). Using the properties of exponents, we subtract the exponent in the denominator from the exponent in the numerator. x^(-7) / x^(-2) = x^(-7-(-2)) = x^(-7+2) = x^(-5)Write Final Expression: Write the final simplified expression. The simplified expression is x^(-5), which can also be written as 1/(x^(5)).

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Select the equivalent expression.

(x^(-7))/(x^(-6)*x^(4))

x^(9)

(1)/(x^(5))

(1)/(x^(9))

x^(5)

Select the equivalent expression. $\newline$ $\frac{x^{-7}}{x^{-6} \cdot x^{4}}$ $\newline$ $x^{9}$ $\newline$ $\frac{1}{x^{5}}$ $\newline$ $\frac{1}{x^{9}}$ $\newline$ $x^{5}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the equivalent expression.

\newline

\frac{x^{-7}}{x^{-6} \cdot x^{4}}

\newline

x^{9}

\newline

\frac{1}{x^{5}}

\newline

\frac{1}{x^{9}}

\newline

x^{5}

Simplify Expression: Simplify the expression using the properties of exponents. $\newline$ We have the expression $(x^{-7})/(x^{-6}\cdot x^{4})$ . 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 Properties: Apply the properties of exponents to the denominator. $\newline$ First, we will simplify the denominator by adding the exponents of $x$ since they are being multiplied together. $\newline$ $x^{-6}$ $x^{4} = x^{-6+4} = x^{-2}$
Divide Numerator: Now, divide the numerator by the simplified denominator. $\newline$ We have $x^{-7}$ divided by $x^{-2}$ . Using the properties of exponents, we subtract the exponent in the denominator from the exponent in the numerator. $\newline$ $x^{-7} / x^{-2} = x^{-7-(-2)} = x^{-7+2} = x^{-5}$
Write Final Expression: Write the final simplified expression. $\newline$ The simplified expression is $x^{-5}$ , which can also be written as $1/(x^{5})$ .