Use the rules of exponents to simplify each exponential expression. Your result cannot contain any negative exponents. Thank you for your help.
(2m^2)^3
(4x^2y^4z^7)^0
8m^6
1
To simplify the exponential expressions, we can use the rules of exponents.
For the first expression, (2m^2)^3:
Step 1: Apply the power of a power rule. Raise the base, 2m^2, to the power of 3: (2m^2)^3 = 2^3 * (m^2)^3.
Step 2: Simplify the base. 2^3 is equal to 8.
Step 3: Simplify the exponent. When raising a power to another power, we multiply the exponents: (m^2)^3 = m^(2*3) = m^6.
Putting it all together, (2m^2)^3 simplifies to 8m^6.
Now, let's move on to the second expression, (4x^2y^4z^7)^0:
The property that states any number (except 0) raised to the power of 0 is equal to 1 is known as the Zero Exponent Rule.
For any non-zero number a, a^0 = 1.
So applying the Zero Exponent Rule, (4x^2y^4z^7)^0 simplifies to 1.