Exponent operations practice HW

Front

What is the quotient rule for exponents?

Back

The quotient rule states that when dividing two powers with the same base, you subtract the exponents: \( \frac{a^m}{a^n} = a^{m-n} \).

Front

Evaluate \( \frac{x^5}{x^{-5}} \) using the quotient rule.

Back

Using the quotient rule, \( \frac{x^5}{x^{-5}} = x^{5 - (-5)} = x^{10} \).

Front

How do you simplify the expression \( x^5 \cdot x^7 \)?

Back

You add the exponents: \( x^5 \cdot x^7 = x^{5+7} = x^{12} \).

Front

What is the product rule for exponents?

Back

The product rule states that when multiplying two powers with the same base, you add the exponents: \( a^m \cdot a^n = a^{m+n} \).

Front

Simplify the expression \( (-4r^5)(2r^8) \).

Back

Multiply the coefficients and add the exponents: \( (-4)(2) = -8 \) and \( r^{5+8} = r^{13} \), so the result is \( -8r^{13} \).

Front

What is an exponent?

Back

An exponent is a number that indicates how many times to multiply the base by itself. For example, in \( 4^2 \), the exponent is 2, meaning \( 4 \times 4 \).

Front

Evaluate \( \frac{y^7}{y^2} \) using the quotient rule.

Back

Using the quotient rule, \( \frac{y^7}{y^2} = y^{7-2} = y^5 \).

Front

What is the zero exponent rule?

Back

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

Front

What happens when you raise a power to another power?

Back

When raising a power to another power, you multiply the exponents: \( (a^m)^n = a^{m imes n} \).

Front

Simplify \( (x^3)^4 \).

Back

Using the power of a power rule, \( (x^3)^4 = x^{3 imes 4} = x^{12} \).