3/17 Alg1: Properties of Exponents

Please rate your current state of understanding of the learning target.

Learning Target: I can solve equations with rational exponents.

What does  $3^{\frac{1}{2}}$  equal?

What does $2^{\frac{1}{3}}$  equal?

Consider the equation $\left(3^{\frac{x}{2}}\right)\left(3^{\frac{x}{3}}\right)=3^9$  .

Which property of exponents does this look like we will use to solve for x?

Consider the equation $\left(3^{\frac{x}{2}}\right)\left(3^{\frac{x}{3}}\right)=3^9$  .

What does the product of powers property tell us to do first if we want to solve for x?

Consider the equation $\left(3^{\frac{x}{2}}\right)\left(3^{\frac{x}{3}}\right)=3^9$  .

Use the Product of Powers property to solve for x.

Consider the equation $\left(2^{\frac{x}{4}}\right)\left(2^{\frac{x}{6}}\right)=2^3$  .

Use the Product of Powers property to solve for x.

 Consider the equation: $27^{\left(x-4\right)}=3^{\left(2x-6\right)}$ 


Which property of exponents does this look like we will use to solve for x?

Please rate your current state of understanding of the learning target.

Learning Target: I can solve equations with rational exponents.