Properties of Exponents: Product and Power

Front

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

Back

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

Front

What is the power of a power rule in exponents?

Back

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

Front

How do you simplify the expression (8^5)^3?

Back

(8^5)^3 = 8^(5*3) = 8^15.

Front

What is the result of multiplying (6p^2q^3) and (4pq)?

Back

(6p^2q^3)(4pq) = 24p^(2+1)q^(3+1) = 24p^3q^4.

Front

How do you find the area of a rectangle given height and width in terms of variables?

Back

Area = height * width. For height = 5x^2y^7 and width = 3x^3y, Area = 15x^(2+3)y^(7+1) = 15x^5y^8.

Front

What is the result of multiplying (4x^5y^2) and (6x^2y^3)?

Back

(4x^5y^2)(6x^2y^3) = 24x^(5+2)y^(2+3) = 24x^7y^5.

Front

What does it mean if an expression is true or false in the context of exponents?

Back

True or false questions in exponents often check understanding of exponent rules or properties.

Front

What is the zero exponent rule?

Back

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

Front

What is the negative exponent rule?

Back

A negative exponent indicates the reciprocal: a^(-n) = 1/(a^n).

Front

How do you simplify the expression a^m * a^n?

Back

Add the exponents: a^m * a^n = a^(m+n).