exponent operations

Front

What is the quotient of powers rule in exponent operations?

Back

The quotient of powers rule states that when dividing two expressions with the same base, you subtract the exponents: a^m / a^n = a^(m-n).

Front

How do you simplify the expression \( \frac{10p^4}{6p} \)?

Back

To simplify \( \frac{10p^4}{6p} \), divide the coefficients (10/6 = 5/3) and subtract the exponents of p (4-1 = 3), resulting in \( \frac{5p^3}{3} \).

Front

What is the product of powers rule in exponent operations?

Back

The product of powers rule states that when multiplying two expressions with the same base, you add the exponents: a^m * a^n = a^(m+n).

Front

How do you simplify the expression \( 7v^3 \cdot 10u^3v^5 \)?

Back

To simplify \( 7v^3 \cdot 10u^3v^5 \), multiply the coefficients (7*10 = 70) and add the exponents of v (3+5 = 8), resulting in \( 70u^3v^8 \).

Front

What is the power of a power rule in exponent operations?

Back

The power of a power rule states that when raising a power to another power, you multiply the exponents: (a^m)^n = a^(m*n).

Front

How do you simplify the expression \( (3a^2)^2 \)?

Back

To simplify \( (3a^2)^2 \), square the coefficient (3^2 = 9) and multiply the exponents of a (2*2 = 4), resulting in \( 9a^4 \).

Front

What is the zero exponent rule in exponent operations?

Back

The zero exponent rule states that any non-zero base raised to the power of zero equals one: a^0 = 1 (where a ≠ 0).

Front

What happens when you have a negative exponent?

Back

A negative exponent indicates the reciprocal of the base raised to the opposite positive exponent: a^(-n) = 1/(a^n) (where a ≠ 0).

Front

How do you evaluate the expression \( a^2b^7 \) using the quotient of powers rule?

Back

Using the quotient of powers rule, if you have a^m / a^n, you subtract the exponents. For example, a^2b^7 can be seen as a^2 / a^0 (since b has no exponent), resulting in a^2b^7.

Front

What is the definition of an exponent?

Back

An exponent indicates how many times a base is multiplied by itself. For example, a^n means 'a' is multiplied by itself 'n' times.