### Home > CCAA8 > Chapter 5 Unit 6 > Lesson CCA: 5.1.1 > Problem5-10

5-10.

Simplify each expression below. Assume that the denominator in part (b) is not equal to zero.

1. $( x ^ { 3 } ) ( x ^ { - 2 } )$

• What do the exponents mean? Is there a shortcut?

• ${\frac{x\cdot x\cdot x}{x\cdot x}}$

1. $4 ^ { - 1 }$

• What do the exponents mean?

• $\text{For example: }y^{-3}=\frac{1}{y^{3}}$

• Now how can you simplify the given problem?

1. $\quad \frac { y ^ { 5 } } { y ^ { - 2 } }$

• Interpret the meaning of the exponents
$(y·y·y·y·y)(y·y)$, then simplify.
What is the shortcut?

1. $(4x^2)^3$

• Remember what each exponent means.

• $64x^6$