Questions: Simplify: (5^23 cdot 5^15)

Solution Steps

To simplify the expression \(5^{23} \cdot 5^{15}\), we can use the product property of exponents, which states that when multiplying two powers with the same base, you add the exponents. Therefore, the expression simplifies to \(5^{23+15}\).

To simplify the expression \(5^{23} \cdot 5^{15}\), we use the product property of exponents, which states: \[ a^m \cdot a^n = a^{m+n} \] Thus, we can rewrite the expression as: \[ 5^{23} \cdot 5^{15} = 5^{23 + 15} = 5^{38} \]

Next, we compute the value of \(5^{38}\). The result of this calculation is: \[ 5^{38} = 363797880709171295166015625 \]

Final Answer