### Home > AC > Chapter 14 > Lesson 14.2.1.1 > Problem2-10

2-10.

Simplify each expression below. Be sure to show your work. (Hint: Use your understanding of the meaning of exponents to expand each expression and then simplify.) Assume that the denominators in parts (b) and (c) are not equal to zero.

1. $\left(x^{3}\right)\left(x^{2}\right)$

Interpret the meaning of the exponents $\left(x· x · x\right)\left(x · x\right)$, then simplify. What is the shortcut?

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

What do the exponents mean? Is there a shortcut?

$\frac{y \cdot y \cdot y \cdot y \cdot y}{y\cdot y}$

1. $\frac { x ^ { 3 } } { x ^ { 7 } }$

What do the exponents mean?

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

Now how can you simplify the given problem?

1. $\left(x^{2}\right)^{3}$

Remember what each exponent means.

$x^{6}$