Select the equivalent expression. (x^(-8)*x^(-7))/(x^(-5)) x^(10) x^(4) (1)/(x^(4)) (1)/(x^(10))

Simplify Exponents: Simplify the numerator using the product of powers property. The product of powers property states that when you multiply two exponents with the same base, you add the exponents. So, x^(-8) * x^(-7) becomes x^(-8 + -7). Calculate the sum of the exponents. -8 + -7 = -15 So, x^(-8) * x^(-7) = x^(-15)Divide Exponents: Divide the numerator by the denominator using the quotient of powers property. The quotient of powers property states that when you divide two exponents with the same base, you subtract the exponents. So, x^(-15) / x^(-5) becomes x^(-15 - (-5)). Calculate the difference of the exponents. -15 - (-5) = -15 + 5 = -10 So, x^(-15) / x^(-5) = x^(-10)Write Final Expression: Write the final expression. The expression x^(-10) can be written as 1/(x^(10)). This is because a negative exponent indicates the reciprocal of the base raised to the positive of that exponent. So, the equivalent expression is 1/(x^(10)).

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Select the equivalent expression.

(x^(-8)*x^(-7))/(x^(-5))

x^(10)

x^(4)

(1)/(x^(4))

(1)/(x^(10))

Select the equivalent expression. $\newline$ $\frac{x^{-8} \cdot x^{-7}}{x^{-5}}$ $\newline$ $x^{10}$ $\newline$ $x^{4}$ $\newline$ $\frac{1}{x^{4}}$ $\newline$ $\frac{1}{x^{10}}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the equivalent expression.

\newline

\frac{x^{-8} \cdot x^{-7}}{x^{-5}}

\newline

x^{10}

\newline

x^{4}

\newline

\frac{1}{x^{4}}

\newline

\frac{1}{x^{10}}

Simplify Exponents: Simplify the numerator using the product of powers property. $\newline$ The product of powers property states that when you multiply two exponents with the same base, you add the exponents. $\newline$ So, $x^{-8} \times x^{-7}$ becomes $x^{(-8 + -7)}$ . $\newline$ Calculate the sum of the exponents. $\newline$ $-8 + -7 = -15$ $\newline$ So, $x^{-8} \times x^{-7} = x^{-15}$
Divide Exponents: Divide the numerator by the denominator using the quotient of powers property. $\newline$ The quotient of powers property states that when you divide two exponents with the same base, you subtract the exponents. $\newline$ So, $x^{-15} / x^{-5}$ becomes $x^{-15 - (-5)}$ . $\newline$ Calculate the difference of the exponents. $\newline$ $-15 - (-5) = -15 + 5 = -10$ $\newline$ So, $x^{-15} / x^{-5} = x^{-10}$
Write Final Expression: Write the final expression. $\newline$ The expression $x^{-10}$ can be written as $1/(x^{10})$ . $\newline$ This is because a negative exponent indicates the reciprocal of the base raised to the positive of that exponent. $\newline$ So, the equivalent expression is $1/(x^{10})$ .