use the power rule of exponents to create a simplified equivalent expression (19 to the power of 4) to the power of 9
To simplify the expression (19^4)^9 using the power rule of exponents, we need to raise the base 19 to the power of 4 and then raise the result to the power of 9.
Step 1: Raise the base 19 to the power of 4
19^4 = 19 * 19 * 19 * 19 = 130,321
Step 2: Raise the result from Step 1 to the power of 9
(19^4)^9 = 130,321^9
Therefore, the simplified equivalent expression for (19^4)^9 is 130,321^9.
To simplify the expression (19^4)^9 using the power rule of exponents, we need to multiply the exponents.
First, let's simplify (19^4):
(19^4) = 19 * 19 * 19 * 19 = 130,321
Now, we can raise this simplified expression to the power of 9:
(130,321)^9 = 130,321 * 130,321 * 130,321 * 130,321 * 130,321 * 130,321 * 130,321 * 130,321 * 130,321
To multiply these numbers together, we simply add their exponents:
(130,321)^9 = (130,321)^(1+1+1+1+1+1+1+1+1)
= (130,321)^9
= 4,012,304,659,710,082,665,741,801,184,401
Therefore, the simplified equivalent expression is 4,012,304,659,710,082,665,741,801,184,401.
To simplify the expression (19^4)^9 using the power rule of exponents, we need to multiply the exponents together.
The power rule of exponents states that when you raise a power to another power, you multiply the exponents. In this case, we have (19^4)^9, where the base is 19 and the first exponent is 4. We need to raise 19^4 to the power of 9.
To simplify, we multiply the exponents: 4 × 9 = 36.
Therefore, (19^4)^9 simplifies to 19^36.