Properties of Exponents

Front

Define the property of exponents: \( a^m \cdot a^n \)

Back

The property states that when multiplying two powers with the same base, you add the exponents: \( a^m \cdot a^n = a^{m+n} \).

Front

What is the result of \( a^0 \) for any non-zero number \( a \)?

Back

The result is 1. That is, \( a^0 = 1 \) for any non-zero \( a \).

Front

Simplify the expression: \( \frac{x^{-7}}{x^4} \)

Back

The simplified expression is \( \frac{1}{x^{11}} \).

Front

What is the value of \( (5^3 x^2 y^4)^0 \)?

Back

The value is 1, since any non-zero expression raised to the power of 0 equals 1.

Front

Simplify the expression: \( (12x^3y)^2 \)

Back

The simplified expression is \( 144x^6y^2 \).

Front

What is the result of \( (2x^3y)^6 \)?

Back

The result is \( 64x^{18}y^6 \).

Front

Define the property of exponents: \( \frac{a^m}{a^n} \)

Back

The property states that when dividing two powers with the same base, you subtract the exponents: \( \frac{a^m}{a^n} = a^{m-n} \).

Front

What happens when you raise a power to a power, such as \( (a^m)^n \)?

Back

You multiply the exponents: \( (a^m)^n = a^{m \cdot n} \).

Front

What is the simplified form of \( x^{-3} \)?

Back

The simplified form is \( \frac{1}{x^3} \).

Front

If \( a = 2 \) and \( b = 3 \), what is the value of \( a^2 \cdot b^3 \)?

Back

The value is \( 2^2 \cdot 3^3 = 4 \cdot 27 = 108 \).