Exponents Multiplying, Dividing, Power to Power

Front

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

Back

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

Front

What is the quotient of two exponents with the same base?

Back

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

Front

What is the power of a power rule in exponents?

Back

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

Front

How do you simplify the expression (2x^2y^3)(-4xy)^2?

Back

First, simplify (-4xy)^2 to get 16x^2y^2. Then multiply: (2x^2y^3)(16x^2y^2) = 32x^(2+2)y^(3+2) = 32x^4y^5.

Front

What is the simplified form of (7a^2)(5a^6b)^2?

Back

First, simplify (5a^6b)^2 to get 25a^{12}b^2. Then multiply: (7a^2)(25a^{12}b^2) = 175a^(2+12)b^2 = 175a^14b^2.

Front

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

Back

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

Front

What is the value of 2^2?

Back

2^2 = 4.

Front

How do you simplify the expression 2^2 z^7?

Back

The expression is already simplified. It represents 4z^7.

Front

What is the zero exponent rule?

Back

Any non-zero base raised to the power of zero equals one. For example, a^0 = 1 (where a ≠ 0).

Front

What is the negative exponent rule?

Back

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