Exponent Rules Practice

Front

What is the rule for raising a product to a power?

Back

When raising a product to a power, apply the exponent to each factor. For example, \( (ab)^n = a^n b^n \).

Front

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

Back

Any non-zero number raised to the power of 0 is always 1.

Front

Simplify the expression \( (m^3)^5 \).

Back

Using the power of a power rule, \( (m^3)^5 = m^{3 \cdot 5} = m^{15} \).

Front

How do you simplify \( \frac{7^6}{7} \)?

Back

Using the quotient rule, \( \frac{7^6}{7} = 7^{6-1} = 7^5 \).

Front

What is the simplified form of \( (a^4b^{-2})^{-1} \cdot a^2b^3 \)?

Back

First, apply the negative exponent: \( (a^4b^{-2})^{-1} = a^{-4}b^{2} \). Then multiply: \( a^{-4}b^{2} \cdot a^2b^3 = a^{-4+2}b^{2+3} = a^{-2}b^5 \).

Front

What is the power of a power rule?

Back

The power of a power rule states that \( (a^m)^n = a^{m \cdot n} \).

Front

What is the product of powers rule?

Back

The product of powers rule states that \( a^m \cdot a^n = a^{m+n} \).

Front

What is the quotient of powers rule?

Back

The quotient of powers rule states that \( \frac{a^m}{a^n} = a^{m-n} \).

Front

What happens when you raise a power to a negative exponent?

Back

Raising a power to a negative exponent means taking the reciprocal: \( a^{-n} = \frac{1}{a^n} \).

Front

What is the simplified form of \( (2x^3y^2)^2 \)?

Back

Using the power of a product rule: \( (2x^3y^2)^2 = 2^2 \cdot (x^3)^2 \cdot (y^2)^2 = 4x^6y^4 \).