Powers (Multiplying, Dividing, Power to a Power)

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

How do you simplify \( \frac{30y^{12}}{15y^2} \)?

Back

To simplify, divide the coefficients (30/15 = 2) and subtract the exponents of y (12-2 = 10), resulting in \( 2y^{10} \).

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

How do you simplify \( (5ab^2)^2 \)?

Back

Use the power of a product rule: square the coefficient (5^2 = 25) and multiply the exponents of each variable: \( a^1 \to a^{2} \) and \( b^2 \to b^{4} \), resulting in \( 25a^2b^4 \).

Front

Are \( 2^2 \) and \( (-2)^2 \) equivalent?

Back

Yes, both evaluate to 4.

Front

What is the power of a power rule for exponents?

Back

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

Front

How do you evaluate \( 9^7 \cdot 9^9 \)?

Back

Use the product rule: add the exponents (7 + 9 = 16), resulting in \( 9^{16} \).

Front

What is the value of \( a^0 \) for any non-zero number a?

Back

For any non-zero number \( a \), \( a^0 = 1 \).

Front

How do you simplify \( \frac{a^5}{a^2} \)?

Back

Use the quotient rule: subtract the exponents (5 - 2 = 3), resulting in \( a^{3} \).

Front

What happens when you multiply two powers with different bases?

Back

You cannot combine them using the product rule; you must evaluate each power separately.