Multiplying and Dividing Powers

Front

What is a power in mathematics?

Back

A power is a way to express repeated multiplication of a number by itself. It is written in the form a^n, where 'a' is the base and 'n' is the exponent.

Front

What does it mean to multiply powers with the same base?

Back

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

Front

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

Back

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

Front

What is the value of 2^3?

Back

2^3 = 2 * 2 * 2 = 8.

Front

What is the value of 5^0?

Back

Any non-zero number raised to the power of 0 is 1. Therefore, 5^0 = 1.

Front

What is the product of 3^2 and 3^4?

Back

3^2 * 3^4 = 3^(2+4) = 3^6 = 729.

Front

What is the quotient of 10^5 and 10^2?

Back

10^5 / 10^2 = 10^(5-2) = 10^3 = 1000.

Front

What is the power of a power rule?

Back

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

Front

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

Back

(2^3)^2 = 2^(3*2) = 2^6 = 64.

Front

What does it mean to have a negative exponent?

Back

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