Algebra: Check for Understanding - Laws of exponents

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

What is the value of any non-zero number raised to the power of 0?

Back

Any non-zero number raised to the power of 0 is equal to 1: \( a^0 = 1 \) for \( a \neq 0 \).

Front

Simplify the expression \((2ab^2)^3\).

Back

\((2ab^2)^3 = 8a^3b^6\).

Front

What is the result of \(y^{-11} \cdot y^5\)?

Back

Using the product rule, \(y^{-11} \cdot y^5 = y^{-11+5} = y^{-6} = \frac{1}{y^6}\).

Front

Simplify the expression \((3t^2)^3\).

Back

\((3t^2)^3 = 27t^6\).

Front

What does the Negative Exponent Rule state?

Back

The Negative Exponent Rule states that \( a^{-n} = \frac{1}{a^n} \).

Front

If \(a^m \cdot a^n\) is simplified, what is the result?

Back

Using the product rule, \(a^m \cdot a^n = a^{m+n}\).

Front

What is the value of \(9^5\) when evaluated?

Back

The value of \(9^5\) is 59049.

Front

What is the result of \( \frac{9^9}{9^5} \)?

Back

Using the quotient rule, \( \frac{9^9}{9^5} = 9^{9-5} = 9^4 \).

Front

What is the value of \((-5.7)^0\)?

Back

The value of \((-5.7)^0\) is 1.