Properties of Exponents

Front

What is the area of a rectangle with side lengths 4cd² and 3c⁴d⁵?

Back

The area is calculated as length x width: 4cd² * 3c⁴d⁵ = 12c⁵d⁷.

Front

What is the simplified form of 6⁻⁴?

Back

The simplified form is \frac{1}{6^4}.

Front

How do you simplify (6b⁴c²)²?

Back

Using the power of a product rule: (6b⁴c²)² = 6²b^{4*2}c^{2*2} = 36b^8c^4.

Front

What is the value of n in the expression (x⁸)(x³)⁻² = xⁿ?

Back

n = 2.

Front

What is the simplified form of 2x⁰y³?

Back

Since x⁰ = 1, the expression simplifies to 2y³.

Front

What is the product of x² and x⁴?

Back

Using the product of powers rule: x² * x⁴ = x^{2+4} = x⁶.

Front

What is the quotient of x⁵ and x²?

Back

Using the quotient of powers rule: x⁵ / x² = x^{5-2} = x³.

Front

What is the value of 6²?

Back

6² = 36.

Front

What does it mean to have a negative exponent?

Back

A negative exponent indicates the reciprocal: a⁻ⁿ = \frac{1}{a^n}.

Front

What is the simplified form of (x²y³)⁴?

Back

Using the power of a product rule: (x²y³)⁴ = x^{2*4}y^{3*4} = x^8y^{12}.