Multiplying Exponents

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

How do you simplify the expression (4y^7) * (-10y^{-2})?

Back

To simplify, multiply the coefficients (4 * -10 = -40) and add the exponents of y (7 + (-2) = 5). The result is -40y^5.

Front

What is the result of multiplying (-7y^2) and (5y^4)?

Back

Multiply the coefficients (-7 * 5 = -35) and add the exponents of y (2 + 4 = 6). The result is -35y^6.

Front

What is the rule for multiplying exponents with different bases?

Back

When multiplying exponents with different bases, you cannot combine them. You simply write them as a product, e.g., a^m * b^n.

Front

How do you simplify the expression (5a^3b^5) * (-8ab)?

Back

Multiply the coefficients (5 * -8 = -40) and add the exponents of a (3 + 1 = 4) and b (5 + 1 = 6). The result is -40a^4b^6.

Front

What is the result of (-5^3) * (-5^8) * (-5^{-2})?

Back

Add the exponents: -3 + 8 + (-2) = 3. The result is -5^3.

Front

What happens when you multiply a positive exponent by a negative exponent?

Back

When multiplying a positive exponent by a negative exponent, you add the exponents. For example, a^m * a^{-n} = a^(m-n).

Front

What is the significance of a negative exponent?

Back

A negative exponent indicates the reciprocal of the base raised to the absolute value of the exponent. For example, a^{-n} = 1/(a^n).

Front

How do you handle coefficients when multiplying expressions with exponents?

Back

Multiply the coefficients separately from the variables. For example, in (3x^2)(4x^3), multiply 3 and 4 to get 12, and add the exponents of x to get x^(2+3) = x^5.

Front

What is the result of simplifying (3g^2h^3) * (-2gh)?

Back

Multiply the coefficients (3 * -2 = -6) and add the exponents of g (2 + 1 = 3) and h (3 + 1 = 4). The result is -6g^3h^4.