Question

1. target a an expression is shown. fully simplify the expression. \\(\frac{(x^{3})^{2}y^{7}}{xy^{2}}\\) use powers in tools (σ) below to write in correct notation

Explanation:

Step1: Simplify the numerator's exponent

First, simplify \((x^{3})^{2}\) using the power of a power rule \((a^{m})^{n}=a^{mn}\). So \((x^{3})^{2}=x^{3\times2}=x^{6}\). Now the expression becomes \(\frac{x^{6}y^{7}}{xy^{2}}\).

Step2: Simplify the x - terms

For the \(x\) - terms, use the quotient rule of exponents \(\frac{a^{m}}{a^{n}}=a^{m - n}\). Here, for \(x\) we have \(\frac{x^{6}}{x^{1}}=x^{6-1}=x^{5}\) (since \(x = x^{1}\)).

Step3: Simplify the y - terms

For the \(y\) - terms, use the quotient rule of exponents \(\frac{y^{7}}{y^{2}}=y^{7 - 2}=y^{5}\).

Answer:

\(x^{5}y^{5}\)