Simplifying Expressions with Exponents

Front

What is the definition of an exponent?

Back

An exponent is a number that indicates how many times to multiply the base by itself.

Front

What does it mean to simplify an expression with exponents?

Back

To simplify an expression with exponents means to reduce it to its simplest form, combining like terms and applying exponent rules.

Front

What is the product of powers rule?

Back

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

Front

What is the power of a power rule?

Back

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

Front

What is the power of a product rule?

Back

When raising a product to a power, apply the exponent to each factor: (ab)^n = a^n * b^n.

Front

What is the zero exponent rule?

Back

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

Front

What is the negative exponent rule?

Back

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

Front

Simplify: (2x^3)(3x^2)

Back

6x^5.

Front

Simplify: (x^4)(x^3)

Back

x^7.

Front

Simplify: (5y^2)(-2y^5)

Back

-10y^7.