Simplifying Exponents

Front

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

Back

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

Front

What is the value of any non-zero number raised to the power of 0?

Back

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

Front

What is the power of a power rule in exponents?

Back

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

Front

Simplify the expression: (3x^2)(4x^3)

Back

12x^5 (Multiply the coefficients and add the exponents of x).

Front

What is the quotient rule for exponents?

Back

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

Front

Simplify the expression: x^8 / x^3

Back

x^5 (Subtract the exponents: 8 - 3 = 5).

Front

What happens when you raise a product to a power?

Back

When raising a product to a power, raise each factor to that power. For example, (ab)^n = a^n * b^n.

Front

Simplify the expression: (2^3)(2^2)

Back

2^5 (Add the exponents: 3 + 2 = 5).

Front

What is the value of (x^0)?

Back

x^0 = 1 for any non-zero x.

Front

Simplify the expression: (5^2)^3

Back

5^6 (Multiply the exponents: 2 * 3 = 6).