Rules of exponents

Front

What is the rule for converting a negative exponent to a positive exponent?

Back

To convert a negative exponent to a positive exponent, take the reciprocal of the base raised to the positive exponent. For example, a^(-n) = 1/(a^n).

Front

Simplify the expression x^5 * x^7.

Back

x^(5+7) = x^12.

Front

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

Back

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

Front

Simplify (2a^2b^4z)(6a^3b^2z^5).

Back

12a^(2+3)b^(4+2)z^(1+5) = 12a^5b^6z^6.

Front

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

Back

When multiplying powers with the same base, add the exponents.

Front

Simplify (-2)^3 * (-2)^6.

Back

(-2)^(3+6) = (-2)^9.

Front

What is the rule for dividing powers with the same base?

Back

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

Front

Simplify the expression 10x^(-2).

Back

10/x^2.

Front

What is the rule for raising a power to another power?

Back

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

Front

Simplify the expression (x^2)^3.

Back

x^(2*3) = x^6.