Simplify: $3^{4} \times 3^{6}$
Simplify: $5^{9} \div 5^{4}$
Simplify: $(2^{5})^{3}$
Simplify: $(xy)^{5}$
Simplify: $(4a)^{3}$
Simplify: $(3x^{2})^{2}$
Simplify: $(abc)^{3}$
Simplify: $(\frac{a}{b})^{4}$
Simplify: $(\frac{3x}{2y})^{2}$
Find the value of: $12^{0}$
Simplify: $3^{4} \times 3^{6}$
Result: $3^{10}$
Explanation: Use the Product Rule. When multiplying terms with the same base, add the exponents: $4 + 6 = 10$.
Simplify: $5^{9} \div 5^{4}$
Result: $5^{5}$
Explanation: Use the Quotient Rule. When dividing terms with the same base, subtract the exponent of the divisor from the exponent of the dividend: $9 – 4 = 5$.
Simplify: $(2^{5})^{3}$
Result: $2^{15}$
Explanation: Use the Power of a Power Rule. Multiply the exponents together: $5 \times 3 = 15$.
Simplify: $(xy)^{5}$
Result: $x^{5}y^{5}$
Explanation: Use the Power of a Product Rule. Distribute the exponent to every factor inside the parentheses.
Simplify: $(4a)^{3}$
Result: $64a^{3}$
Explanation: Distribute the cube to both the coefficient and the variable: $4^{3} \times a^{3}$. Since $4 \times 4 \times 4 = 64$, the result is $64a^{3}$.
Simplify: $(3x^{2})^{2}$
Result: $9x^{4}$
Explanation: Apply the exponent to the 3 ($3^{2} = 9$) and use the Power of a Power rule for the variable ($x^{2 \times 2} = x^{4}$).
Simplify: $(abc)^{3}$
Result: $a^{3}b^{3}c^{3}$
Explanation: Similar to problem 4, the exponent is applied to each individual factor within the parentheses.
Simplify: $(\frac{a}{b})^{4}$
Result: $\frac{a^{4}}{b^{4}}$
Explanation: Use the Power of a Quotient Rule. The exponent applies to both the numerator and the denominator.
Simplify: $(\frac{3x}{2y})^{2}$
Result: $\frac{9x^{2}}{4y^{2}}$
Explanation: Square every term in the fraction: $3^{2} = 9$, $x$ becomes $x^{2}$, $2^{2} = 4$, and $y$ becomes $y^{2}$.
Find the value of: $12^{0}$
Result: $1$
Explanation: Use the Zero Exponent Rule. Any non-zero number raised to the power of zero is always 1.