Simplify. (8x^(5)y^(-1))/(4y^(8))

Simplify coefficients: Simplify the coefficients and separate the variables. We have the expression (8x^(5)y^(-1))/(4y^(8)). First, we simplify the numerical coefficients by dividing 8 by 4. 8/4 = 2 Now we have 2x^(5)y^(-1)/y^(8).Apply quotient rule: Apply the quotient rule for exponents. The quotient rule states that when we divide like bases, we subtract the exponents. For the variable x, we only have x^(5) in the numerator, so it remains as is. For the variable y, we have y^(-1) in the numerator and y^(8) in the denominator. We subtract the exponents: (-1) - 8 = -9. Now we have 2x^(5)y^(-9).Rewrite negative exponents: Rewrite negative exponents as positive exponents in the denominator. A negative exponent means that the base is on the wrong side of the fraction line, so we move y^(-9) to the denominator to make it a positive exponent. Now we have 2x^(5)/y^(9).

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Simplify. $\newline$ $\left(\frac{8x^{5}y^{-1}}{4y^{8}}\right)$

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Algebra 1

Evaluate integers raised to rational exponents

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Q. Simplify.

\newline

\left(\frac{8x^{5}y^{-1}}{4y^{8}}\right)

Simplify coefficients: Simplify the coefficients and separate the variables. $\newline$ We have the expression $(8x^{5}y^{-1})/(4y^{8})$ . First, we simplify the numerical coefficients by dividing $8$ by $4$ . $\newline$ $8/4 = 2$ $\newline$ Now we have $2x^{5}y^{-1}/y^{8}$ .
Apply quotient rule: Apply the quotient rule for exponents. The quotient rule states that when we divide like bases, we subtract the exponents. For the variable $x$ , we only have $x^{5}$ in the numerator, so it remains as is. For the variable $y$ , we have $y^{-1}$ in the numerator and $y^{8}$ in the denominator. We subtract the exponents: $(-1) - 8 = -9$ . Now we have $2x^{5}y^{-9}$ .
Rewrite negative exponents: Rewrite negative exponents as positive exponents in the denominator. A negative exponent means that the base is on the wrong side of the fraction line, so we move $y^{-9}$ to the denominator to make it a positive exponent. Now we have $\frac{2x^{5}}{y^{9}}$ .