What is the value of the expression \frac{3^4 \cdot 3^2}{3^3}? — ACT

What is the value of the expression $\frac{3^4 \cdot 3^2}{3^3}$ ?

Evaluating the numerator using the product rule of exponents yields

3^6

. Then, applying the quotient rule of exponents to divide

3^6

3^3

yields

3^3

. Evaluating

3^3

gives

27

Simplify the numerator using the product rule of exponents:

a^m \cdot a^n = a^{m+n}

3^4 \cdot 3^2 = 3^{4+2} = 3^6

When multiplying exponential terms with the same base, add their exponents.

Simplify the fraction using the quotient rule of exponents:

\frac{a^m}{a^n} = a^{m-n}

\frac{3^6}{3^3} = 3^{6-3} = 3^3

When dividing exponential terms with the same base, subtract the exponent in the denominator from the exponent in the numerator.

Evaluate the simplified exponential expression.

3^3 = 3 \cdot 3 \cdot 3 = 27

Evaluate the base raised to the power of 3 by multiplying it by itself three times.

Simplifying expressions using the product and quotient rules of exponents

Estimated Time:45s

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