Exponent Rules

Front

What is the product of powers rule in exponentiation?

Back

When multiplying two powers with the same base, you add the exponents: a^m * a^n = a^(m+n).

Front

How do you simplify the expression x^4 * x^5?

Back

Using the product of powers rule, x^4 * x^5 simplifies to x^(4+5) = x^9.

Front

What is the power of a power rule in exponentiation?

Back

When raising a power to another power, you multiply the exponents: (a^m)^n = a^(m*n).

Front

How do you simplify the expression (2x^2)^3?

Back

Using the power of a power rule, (2x^2)^3 simplifies to 2^3 * (x^2)^3 = 8x^6.

Front

What does it mean to write an expression with positive exponents?

Back

Writing an expression with positive exponents means rewriting any negative exponents as positive by taking the reciprocal of the base.

Front

How do you rewrite a^(-2) with positive exponents?

Back

a^(-2) can be rewritten as 1/a^2.

Front

What is the quotient of powers rule in exponentiation?

Back

When dividing two powers with the same base, you subtract the exponents: a^m / a^n = a^(m-n).

Front

How do you simplify the expression x^6 / x^2?

Back

Using the quotient of powers rule, x^6 / x^2 simplifies to x^(6-2) = x^4.

Front

What is the rule for dividing powers with different bases?

Back

When dividing powers with different bases, you cannot simplify using exponents; you must evaluate each base separately.

Front

How do you simplify the expression (xy^2)^3?

Back

Using the power of a product rule, (xy^2)^3 simplifies to x^3 * (y^2)^3 = x^3 * y^6.