Simplifying Exponential Expressions Warm Up

Front

What is the general rule for simplifying expressions with negative exponents?

Back

For any non-zero number a, a^{-n} = 1/a^{n}. This means that negative exponents can be converted to positive exponents by taking the reciprocal.

Front

How do you simplify an expression with a zero exponent?

Back

For any non-zero number a, a^0 = 1. This means that any base raised to the power of zero equals one.

Front

What is the simplified form of \( \frac{a^m}{a^n} \)?

Back

The simplified form is \( a^{m-n} \). This is based on the property of exponents that states when dividing like bases, you subtract the exponents.

Front

What is the simplified form of \( a^m \cdot a^n \)?

Back

The simplified form is \( a^{m+n} \). This is based on the property of exponents that states when multiplying like bases, you add the exponents.

Front

What does it mean to simplify \( \frac{4}{a^3b^2} \)?

Back

It means to express the fraction in its simplest form, which is already simplified as there are no common factors in the numerator and denominator.

Front

How do you simplify \( (4)^{-2} \)?

Back

Using the rule for negative exponents, \( (4)^{-2} = \frac{1}{4^2} = \frac{1}{16} \).

Front

What is the value of \( x^{-3}y^0 \)?

Back

Since \( y^0 = 1 \), the expression simplifies to \( \frac{1}{x^3} \).

Front

How do you simplify \( 5v^{-2} \)?

Back

Using the rule for negative exponents, \( 5v^{-2} = \frac{5}{v^2} \).

Front

What is the value of \( 6x^0 \)?

Back

Since \( x^0 = 1 \), the expression simplifies to 6.

Front

What is the property of exponents that allows you to simplify \( a^{-n} \)?

Back

The property states that \( a^{-n} = \frac{1}{a^n} \), which allows you to convert negative exponents to positive.