Simplify. Answer should contain only positive exponents. Please show work.
(3a^2)^3
Thank you!!
3^3 * (a^2)^3 = 27 a^6
To simplify the expression (3a^2)^3 and write it with positive exponents, you can use the rule of exponentiation that states "to raise a power to a power, multiply the exponents."
Here's how it works with your expression:
Step 1: Apply the rule by multiplying the exponents:
(3a^2)^3 = 3^3 * (a^2)^3
Step 2: Simplify the base with the exponent of 3:
3^3 = 27
Step 3: Simplify the base of 'a' with the exponent of 2, raised to the power of 3:
(a^2)^3 = a^(2*3) = a^6
Step 4: Combine the simplified bases:
27 * a^6
Therefore, the simplified form of (3a^2)^3 is 27a^6, written with positive exponents.