Exponent Rules

Front

What is the product of two powers with the same base?

Back

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

Front

What is the power of a power rule in exponentiation?

Back

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

Front

How do you simplify the expression 5x^4 * 3x?

Back

You multiply the coefficients (5 * 3 = 15) and add the exponents of x (4 + 1 = 5), resulting in 15x^5.

Front

What is the quotient of powers rule in exponentiation?

Back

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

Front

How do you simplify the expression (x^3/y^4)^5?

Back

You apply the power of a power rule: (x^3)^5 = x^(3*5) = x^15 and (y^4)^5 = y^(4*5) = y^20, resulting in x^15/y^20.

Front

What is the zero exponent rule?

Back

Any non-zero base raised to the power of zero equals one. For example, a^0 = 1 (where a ≠ 0).

Front

How do you simplify the expression x^2 * x^3?

Back

You add the exponents since the bases are the same: x^(2+3) = x^5.

Front

What is the rule for multiplying powers with the same exponent?

Back

When multiplying powers with the same exponent, you multiply the bases. For example, a^m * b^m = (a*b)^m.

Front

How do you simplify the expression x^4 * x^2 * x?

Back

You add the exponents: x^(4+2+1) = x^7.

Front

What is the rule for multiplying powers with different bases but the same exponent?

Back

When multiplying powers with different bases but the same exponent, you can multiply the bases and keep the exponent. For example, a^m * b^m = (a*b)^m.