Simplify expressions involving exponents

Sample Solution

• Power to a power: When a number or variable is raised to a power, and then that entire expression is raised to another power, the powers are multiplied. For example, (x2)3=x2⋅3=x6.
• Product to a power: When a product is raised to a power, each term in the product is raised to the power. For example, (x2y)3=x2⋅3y3⋅1=x6y3.
• Quotient to a power: When a quotient is raised to a power, the numerator and denominator are raised to the power separately. For example, (yx​)3=y3x3​.

Full Answer Section

• Zero to any power: Any number or variable to the zeroth power is one. For example, x0=1.
• Negative power: A number or variable to a negative power is the reciprocal of the number or variable to the positive power of the same absolute value. For example, x−2=x21​.
• Bases of the same power: When the bases of two powers are the same, the powers are equal. For example, x2=x2.

Here are some ways to simplify expressions involving exponents:

• Use the rules for exponents.
• Look for common factors and simplify.
• Factor the expressions.
• Use the distributive property.

Here is how adding and multiplying polynomial expressions differ:

• Adding polynomial expressions: When adding polynomial expressions, you can simply remove the parentheses and combine the like terms. For example, x2+2x+3+x2−x+1=2x2+x+4.
• Multiplying polynomial expressions: When multiplying polynomial expressions, you can use the distributive property. For example, (x2+2x+3)(x−1)=x3−x2+3x−3.

Here are some additional tips for simplifying expressions involving exponents:

• Keep track of the positive and negative signs.
• Be careful not to over simplify.
• Use a calculator to check your work.