Select the equivalent expression. (y^(-8)y^(-6))/(x^(5)x^(3)) x^(8)y^(2) (1)/(x^(8)y^(2)) (1)/(x^(8)y^(14)) x^(8)y^(14)

Simplify numerator: Simplify the numerator by adding the exponents of y. When multiplying powers with the same base, you add the exponents. y^(-8) * y^(-6) = y^(-8 + -6) = y^(-14)Simplify denominator: Simplify the denominator by adding the exponents of x. Similarly, when multiplying powers with the same base, you add the exponents. x^(5) * x^(3) = x^(5 + 3) = x^(8)Write simplified expression: Write the simplified expression. Now we have y^(-14) in the numerator and x^(8) in the denominator. So, the simplified expression is (y^(-14))/(x^(8))Convert negative exponents: Convert negative exponents to positive by taking the reciprocal. A negative exponent indicates that the base is on the wrong side of the fraction line, so we take the reciprocal to make the exponent positive. (y^(-14))/(x^(8)) = (1)/(y^(14)x^(8))

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Select the equivalent expression.

(y^(-8)y^(-6))/(x^(5)x^(3))

x^(8)y^(2)

(1)/(x^(8)y^(2))

(1)/(x^(8)y^(14))

x^(8)y^(14)

Select the equivalent expression. $\newline$ $\frac{y^{-8} y^{-6}}{x^{5} x^{3}}$ $\newline$ $x^{8} y^{2}$ $\newline$ $\frac{1}{x^{8} y^{2}}$ $\newline$ $\frac{1}{x^{8} y^{14}}$ $\newline$ $x^{8} y^{14}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the equivalent expression.

\newline

\frac{y^{-8} y^{-6}}{x^{5} x^{3}}

\newline

x^{8} y^{2}

\newline

\frac{1}{x^{8} y^{2}}

\newline

\frac{1}{x^{8} y^{14}}

\newline

x^{8} y^{14}

Simplify numerator: Simplify the numerator by adding the exponents of $y$ . When multiplying powers with the same base, you add the exponents. $y^{-8} \times y^{-6} = y^{-8 + -6}$ = $y^{-14}$
Simplify denominator: Simplify the denominator by adding the exponents of $x$ . Similarly, when multiplying powers with the same base, you add the exponents. $x^{5} \times x^{3} = x^{5 + 3} = x^{8}$
Write simplified expression: Write the simplified expression. $\newline$ Now we have $y^{-14}$ in the numerator and $x^{8}$ in the denominator. $\newline$ So, the simplified expression is $(y^{-14})/(x^{8})$
Convert negative exponents: Convert negative exponents to positive by taking the reciprocal. $\newline$ A negative exponent indicates that the base is on the wrong side of the fraction line, so we take the reciprocal to make the exponent positive. $\newline$ $(y^{-14})/(x^{8}) = (1)/(y^{14}x^{8})$