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Factoring Completely Factor the expression completely.$t^{3}+1$

When does an extraneous solution occur? How can an extraneous solution be recognized?

For the following exercises, use like bases to solve the exponential equation.$$4^{-3 v-2}=4^{-v}$$

For the following exercises, use like bases to solve the exponential equation.$$3^{2 x+1} \cdot 3^{x}=243$$

For the following exercises, use like bases to solve the exponential equation.$$625 \cdot 5^{3 x+3}=125$$

For the following exercises, use like bases to solve the exponential equation.$$\left(\frac{1}{64}\right)^{3 n} \cdot 8=2^{6}$$