Fully simplify using only positive exponents. (5x^(8)y^(7))/(15x^(6)y^(7)) Answer:

Write Expression, Identify Like Terms: Write down the expression and identify like terms. (5x^(8)y^(7))/(15x^(6)y^(7)) We have like terms in the numerator and the denominator that can be simplified.Simplify Coefficients: Simplify the coefficients (numerical parts) of the expression. Divide the coefficients: 5/15 = 1/3 (1/3)x^(8)y^(7)/(x^(6)y^(7))Apply Quotient Rule for Exponents: Apply the quotient rule for exponents to simplify the variable parts. x^(8)/x^(6) = x^(8-6) = x^(2) y^(7)/y^(7) = y^(7-7) = y^(0) = 1 (since any non-zero number raised to the power of 0 is 1) (1/3)x^(2)(1)Multiply Simplified Parts: Multiply the simplified parts together to get the final answer. (1/3)x^(2) * 1 = (1/3)x^(2)

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Algebra 2

Simplify variable expressions using properties

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Q. Fully simplify using only positive exponents.

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\frac{5 x^{8} y^{7}}{15 x^{6} y^{7}}

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Answer:

Write Expression, Identify Like Terms: Write down the expression and identify like terms. $\newline$ $(5x^{8}y^{7})/(15x^{6}y^{7})$ $\newline$ We have like terms in the numerator and the denominator that can be simplified.
Simplify Coefficients: Simplify the coefficients (numerical parts) of the expression. $\frac{5}{15} = \frac{1}{3}$ $\frac{(\frac{1}{3})x^{8}y^{7}}{x^{6}y^{7}}$
Apply Quotient Rule for Exponents: Apply the quotient rule for exponents to simplify the variable parts. $\newline$ $x^{8}/x^{6} = x^{8-6} = x^{2}$ $\newline$ $y^{7}/y^{7} = y^{7-7} = y^{0} = 1$ (since any non-zero number raised to the power of $0$ is $1$ ) $\newline$ $(1/3)x^{2}(1)$
Multiply Simplified Parts: Multiply the simplified parts together to get the final answer. $\frac{1}{3}x^{2} \times 1 = \frac{1}{3}x^{2}$