91Ó°ÊÓ

Simplify by writing each expression with positive exponents. Assume that all variables represent nonzero real numbers. $$ \frac{(a+b)^{-3}}{(a+b)^{-4}} $$

Subtract. See Example \(\boldsymbol{\delta}\) $$ \begin{aligned} 5 a^{4}-3 a^{3}+2 a^{2}-a+6 \\ -6 a^{4}+a^{3}-a^{2}+a-1 \end{aligned} $$

Simplify by writing each expression with positive exponents. Assume that all variables represent nonzero real numbers. $$ \frac{(x+y)^{-8}}{(x+y)^{-9}} $$

Find each product. $$ 3 y(y+2)^{3} $$

Find each product. $$ -4 t(t+3)^{3} $$

Simplify by writing each expression with positive exponents. Assume that all variables represent nonzero real numbers. $$ \frac{(x+2 y)^{-3}}{(x+2 y)^{-5}} $$

Find each product. $$ -5 r(r+1)^{3} $$

Simplify by writing each expression with positive exponents. Assume that all variables represent nonzero real numbers. $$ \frac{(p-3 q)^{-2}}{(p-3 q)^{-4}} $$

In Objective \(I,\) we showed how \(6^{\circ}\) acts as 1 when it is applied to the product rule, thus motivating the definition of 0 as an exponent. We can also use the quotient rule to motivate this definition. Consider the expression \(\frac{25}{25} .\) What is its simplest form?

In Objective \(I,\) we showed how \(6^{\circ}\) acts as 1 when it is applied to the product rule, thus motivating the definition of 0 as an exponent. We can also use the quotient rule to motivate this definition. Because \(25=5^{2},\) the expression \(\frac{25}{25}\) can be written as the quotient of powers of \(5 .\) Write the expression in this way.