Laws of Exponents Flashcard

Front

What is the law of exponents for multiplying powers with the same base?

Back

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

Front

What is the law of exponents for dividing powers with the same base?

Back

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

Front

What is the law of exponents for raising a power to a power?

Back

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

Front

What is the result of any non-zero number raised to the power of zero?

Back

Any non-zero number raised to the power of zero equals 1: a^0 = 1.

Front

What is the result of a negative exponent?

Back

A negative exponent indicates the reciprocal of the base raised to the opposite positive exponent: a^-n = 1/(a^n).

Front

What is the result of (a^m)(a^n)?

Back

The result is a^(m+n) when multiplying powers with the same base.

Front

What is the result of (a^m)/(a^n)?

Back

The result is a^(m-n) when dividing powers with the same base.

Front

What is the result of (a^m)^n?

Back

The result is a^(m*n) when raising a power to another power.

Front

What is the value of (5^2)^-4?

Back

1/(25^4).

Front

What is the value of (2^3)(2^4)(2^5)?

Back

2^12.