Exponents and Powers

Front

What is an exponent?

Back

An exponent is a number that indicates how many times to multiply the base by itself. For example, in 2^3, 2 is the base and 3 is the exponent, meaning 2 is multiplied by itself 3 times (2 x 2 x 2 = 8).

Front

What does the power rule state when multiplying 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 does the power rule state when 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 5^0?

Back

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

Front

What is the result of (x^3)^2?

Back

According to the power of a power rule, (x^m)^n = x^(m*n). Thus, (x^3)^2 = x^(3*2) = x^6.

Front

Simplify: 2^3 * 2^2

Back

Using the power rule for multiplication, 2^3 * 2^2 = 2^(3+2) = 2^5 = 32.

Front

Simplify: 4^2 / 4^3

Back

Using the power rule for division, 4^2 / 4^3 = 4^(2-3) = 4^(-1) = 1/4.

Front

What is the value of (3xy^6)^4?

Back

Using the power of a product rule, (3xy^6)^4 = 3^4 * x^4 * (y^6)^4 = 81x^4y^24.

Front

What is the simplified form of n^10 / n^3?

Back

Using the power rule for division, n^10 / n^3 = n^(10-3) = n^7.

Front

What does it mean to raise a power to a power?

Back

Raising a power to a power means to multiply the exponents. For example, (a^m)^n = a^(m*n).