Exponent Rules

Front

What is a coefficient in an algebraic expression?

Back

A coefficient is a numerical factor that multiplies a variable in an algebraic expression.

Front

What happens to the exponents when dividing powers with the same base?

Back

When dividing powers with the same base, you subtract the exponents.

Front

Simplify the expression: (a^m)(a^n).

Back

The expression simplifies to a^(m+n).

Front

What is the POWER RULE in exponents?

Back

The POWER RULE states that when raising a power to another power, you multiply the exponents.

Front

Simplify the expression: (x^3)(x^2).

Back

The expression simplifies to x^(3+2) = x^5.

Front

What is the result of (2^3)/(2^1)?

Back

The result is 2^(3-1) = 2^2 = 4.

Front

How do you simplify (3xy)^2 using the POWER RULE?

Back

Using the POWER RULE, (3xy)^2 = 3^2 * x^2 * y^2 = 9x^2y^2.

Front

What is the result of (5p^9q^3)(2pq^7)?

Back

The result is 10p^(9+1)q^(3+7) = 10p^10q^10.

Front

What is the exponent of a variable when it is not explicitly written?

Back

When the exponent of a variable is not explicitly written, it is understood to be 1.

Front

What is the result of x^0?

Back

Any non-zero number raised to the power of 0 is equal to 1.