The expressions are illustrations of algebraic expressions, and the simplified expressions are [tex]\frac{x^{5}y^{3}}{7}[/tex], [tex]\frac{7y^{11}}{4z^{4}}[/tex], [tex]8y^{2}[/tex], [tex]\frac{6}{x^5w^3}[/tex], [tex]64w^{15}\\[/tex] and [tex]y^3[/tex]
How to simplify the expressions
[tex](a)\ \frac{xy}{7x^{-4}y^{-2}}[/tex]
Apply the quotient rule of indices
[tex]\frac{x^{1 + 4}y^{1 + 2}}{7}[/tex]
Simplify the exponents
[tex]\frac{x^{5}y^{3}}{7}[/tex]
Hence, the simplified expression is [tex]\frac{x^{5}y^{3}}{7}[/tex]
[tex](b)\ \frac{7y^6}{4y^{-5}z^{4}}[/tex]
Apply the quotient rule of indices
[tex]\frac{7y^{6+5}}{4z^{4}}[/tex]
Simplify the exponents
[tex]\frac{7y^{11}}{4z^{4}}[/tex]
Hence, the simplified expression is [tex]\frac{7y^{11}}{4z^{4}}[/tex]
[tex](c)\ (x^3y^{-5})(2x^{-4}y^2)(4xy^5)[/tex]
Apply the product rule of indices
[tex]4 * 2x^{-4+3+1}y^{2-5+5}[/tex]
Simplify the exponents
[tex]8x^{0}y^{2}[/tex]
Further, simplify
[tex]8y^{2}[/tex]
Hence, the simplified expression is [tex]8y^{2}[/tex]
[tex](d)\ (xw)(6x^{-6}w^{-4})[/tex]
Apply the product rule of indices
[tex]6x^{-6+1}w^{-4+1}[/tex]
Simplify the exponents
[tex]6x^{-5}w^{-3}[/tex]
Rewrite as:
[tex]\frac{6}{x^5w^3}[/tex]
Hence, the simplified expression is [tex]\frac{6}{x^5w^3}[/tex]
[tex](e)\ (w \cdot 4w^2\cdot w^2)^3[/tex]
Apply the product rule of indices
[tex](4w^{1+2+2})^3[/tex]
Simplify the exponents
[tex](4w^{5})^3[/tex]
Expand
[tex]4^3w^{5*3}[/tex]
Further, simplify
[tex]64w^{15}[/tex]
Hence, the simplified expression is [tex]64w^{15}\\[/tex]
[tex](f)\ (\frac{y^2}{y})^3[/tex]
Apply the quotient rule of indices
[tex](y^{2 - 1})^3[/tex]
Simplify the exponents
[tex](y)^3[/tex]
Remove the bracket
[tex]y^3[/tex]
Hence, the simplified expression is [tex]y^3[/tex]
Read more about algebraic expressions at:
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